New: 98,000+ skills indexed from GitHub repos with 100+ stars · every skill safety-checkedBrowse top skillsTop skills
Esc to closeBrowse all skills
Submit a skillBrowse skills
Submit a skillBrowse skills

Agent skill

Operator Theory

by parcadei in parcadei/Continuous-Claude-v3

Problem-solving strategies for operator theory in functional analysis

MITAuto-check: notesResearch & Science

Install Operator Theory

skills CLI
$ npx skills add parcadei/Continuous-Claude-v3 --skill operator-theory -a claude-code

Project install by default; add -g for ~/.claude/skills/.

GitHub CLI
$ gh skill install parcadei/Continuous-Claude-v3 operator-theory --agent claude-code

Project scope by default; add --scope user for a personal install. Needs GitHub CLI 2.90.0 or later (public preview).

Manual copy
$ git clone --depth 1 https://github.com/parcadei/Continuous-Claude-v3.git skills-src && mkdir -p .claude/skills && cp -r skills-src/.claude/skills/math/functional-analysis/operator-theory .claude/skills/operator-theory && rm -rf skills-src

Use ~/.claude/skills/ instead of .claude/skills for a personal install. The folder must contain SKILL.md.

Claude Code skills documentation · loads skills from .claude/skills/

Facts

Skill name
operator-theory
GitHub stars
3.9k
Used in
2 other repos
Token cost
~879 tokens
SKILL.md length
398 words
Files
1
Skills in repo
141
Repo updated
First seen
Licence
MIT

At a glance

Problem-solving strategies for operator theory in functional analysis

  • Works in 5 steps: Bounded operator verification → Adjoint operator → Spectral Theory → …
  • Tasks that involve Math and symbolic computation
  • SKILL.md covers When to Use, Decision Tree, Tool Commands and Key Techniques, plus 1 more section
  • Calls uv

What it does

Operator Theory is an agent skill from parcadei/Continuous-Claude-v3. Problem-solving strategies for operator theory in functional analysis

Its SKILL.md is about 880 tokens, which your agent loads only when the skill is triggered. It is a single SKILL.md file with no bundled scripts.

It sits in Research & Science, covering Math and symbolic computation. It works with SymPy. The repository describes itself as: Context management for Claude Code. Hooks maintain state via ledgers and handoffs. MCP execution without context pollution. Agent orchestration with isolated context windows. The licence is MIT.

When your agent uses it

  • Tasks that involve Math and symbolic computation

Example prompts

  • “/operator-theory”

Requirements

  • Python 3
  • Pre-approved tools (allowed-tools): Bash, Read

Workflow steps

5 steps, taken from the first numbered list in SKILL.md.

  1. Bounded operator verification
  2. Adjoint operator
  3. Spectral Theory
  4. Compact operators
  5. Spectral Theorem

What it can do on your machine

Read from SKILL.md and the folder at commit d07ff4b. It shows what the files ask for, not the result of running them.

  • Tool permissions

    Pre-approves these tools, so the agent can use them without asking each time:

    • Bash
    • Read

    From allowed-tools in the SKILL.md frontmatter.

  • Runs code

    Shell commands in SKILL.md call:

    • uv

    From the folder's file list and the shell code blocks in SKILL.md.

  • Network

    No URLs in SKILL.md. Its commands use uv, which can reach the network depending on how they are called.

    From URLs in SKILL.md, links to its own repository left out.

  • Credentials

    Names no API keys, tokens, secrets or passwords.

    From names ending in _API_KEY, _TOKEN, _SECRET, _KEY or _PASSWORD in SKILL.md.

Context cost

Operator Theory loads about 879 tokens when it runs. Until then it costs about 21 tokens; SKILL.md has 398 words of instructions outside code blocks.

Always · name and description, kept in context so the agent knows when to use it
~21
When it runs · the whole SKILL.md, loaded when a task matches
~879

Estimates: characters ÷ 4, the usual rule of thumb; real counts depend on the model's tokenizer. Scripts and assets cost tokens only if the agent reads them.

Safety

Auto-check: notes

The automated check noted patterns worth knowing about, such as sudo or a known installer.

  • NotePre-approves every shell command (allowed-tools: Bash)SKILL.md
    allowed-tools: Bash, Read

Automated static check — not a guarantee. Review scripts before installing. It scans the text of SKILL.md for risky patterns (piping downloads into a shell, reading credential files, hidden Unicode, destructive commands); files beside SKILL.md are not scanned.

SKILL.md

The full file from parcadei/Continuous-Claude-v3 at commit d07ff4b, republished under its MIT licence (© parcadei). 398 words, ~879 tokens.

Download SKILL.mdSave it as .claude/skills/operator-theory/SKILL.md (or your agent's skills folder).
name
operator-theory
description
Problem-solving strategies for operator theory in functional analysis
allowed-tools
Bash, Read

Operator Theory

When to Use

Use this skill when working on operator-theory problems in functional analysis.

Decision Tree

  1. Bounded operator verification

    • ||Tx|| <= M||x|| for some M
    • Operator norm: ||T|| = sup{||Tx|| : ||x|| = 1}
    • z3_solve.py prove "operator_bounded"

  2. Adjoint operator

    • <Tx, y> = <x, Ty> defines T
    • For matrices: T* = conjugate transpose
    • sympy_compute.py simplify "<Tx, y> - <x, T*y>"

  3. Spectral Theory

    • Spectrum: sigma(T) = {lambda : T - lambda*I not invertible}
    • Self-adjoint: spectrum is real
    • z3_solve.py prove "self_adjoint_real_spectrum"

  4. Compact operators

    • T compact if T(bounded set) has compact closure
    • Approximable by finite-rank operators
    • sympy_compute.py limit "||T - T_n||" --var n

  5. Spectral Theorem

    • Self-adjoint compact: T = sum(lambda_n * P_n)
    • eigenvalues -> 0, eigenvectors form orthonormal basis

Tool Commands

Z3_Bounded_Operator
bash
uv run python -m runtime.harness scripts/z3_solve.py prove "norm(Tx) <= M*norm(x)"
Sympy_Adjoint
bash
uv run python -m runtime.harness scripts/sympy_compute.py simplify "<Tx, y> - <x, T_star_y>"
Z3_Spectral
bash
uv run python -m runtime.harness scripts/z3_solve.py prove "self_adjoint implies real_spectrum"
Sympy_Compact
bash
uv run python -m runtime.harness scripts/sympy_compute.py limit "norm(T - T_n)" --var n --at oo

Key Techniques

From indexed textbooks:

  • [Introductory Functional Analysis with Applications] Spectral theory is one of the main branches of modern functional analysis and its applications. Roughly speaking, it is concerned with certain inverse operators, their general properties and their relations to the original operators. Such inverse operators arise quite naturally in connection with the problem of solving equations (systems of linear algebraic equations, differential equations, integral equations).
  • [Introductory Functional Analysis with Applications] Unbounded linear operators in Hilb,ert spaces will be considered in Chap. Brief orientation about main content of Chap. We begin with finite dimensional vector spaces.
  • [Introductory Functional Analysis with Applications] Most unbounded linear operators occurring in practical problems are closed or have closed linear extensions (Sec. Unbounded Linear Operators in Hilbert Space The spectrum of a self-adjoint linear operator is real, also in the unbounded case (d. T is obtained by means of the Cayley transform U= (T- iI)(T+ iI)-1 of T (d.
  • [Introductory Functional Analysis with Applications] Compact Operators and Their Spectrum is called a degenerate kernel. Here we may assume each of the two sets {ab· . If an equation (1) with such a kernel has a solution x, show that it must be of the form n x(s' = ji(s) + lot L cjaj(s), jl and the unknown constants must satisfy cj - n lot L ajkCk = Yj' kl where j= 1,···, n.
  • [Introductory Functional Analysis with Applications] As indicated before, our key to the application of complex analysis to spectral theory will be Theorem 7. The theorem states that for every value AoEp(n the resolvent R>. TE B(X, X) on a complex Banach space X has a power series repre- sentation (4) R>.
Show full SKILL.md (9 more words)Show less

Cognitive Tools Reference

See .claude/skills/math-mode/SKILL.md for full tool documentation.

© parcadei, MIT. Rendered from Markdown: HTML in the file is shown as text, images as links, and headings moved down two levels. Raw file

Files

Just SKILL.md in .claude/skills/math/functional-analysis/operator-theory of parcadei/Continuous-Claude-v3.

Open the folder on GitHubat commit d07ff4b

Used in 2 other repositories

We found 2 copies of this SKILL.md (exact, near-identical or edited) in other folders, from 2 other GitHub owners. This page covers the copy in parcadei/Continuous-Claude-v3, which our catalogue first saw on October 7, 2026.

Compare with similar skills

Operator Theory next to the 5 skills that share the most tags, products or categories with it. Stars are the repository's; “used in” counts other GitHub owners with a copy.

Operator Theory compared with similar skills
SkillStarsUsed inTokensAuto-checkLicenceRepo updated
Operator Theory this skillparcadei/Continuous-Claude-v33.9k2 repos~879Automated safety check: NotesMIT
SympyzLanqing/codex-claude-academic-skills4.6k16 repos~3.4kAutomated safety check: PassMIT
Edu Analytic Geometrywy51ai/edulab1.4k1 repos~1.6kAutomated safety check: PassApache-2.0
Edu Solid Geometrywy51ai/edulab1.4k1 repos~1.1kAutomated safety check: PassApache-2.0
Math Toolsananddtyagi/cc-marketplace6872 repos~1.3kAutomated safety check: PassNone
Edu Chem Reactionwy51ai/edulab1.4k—~1.2kAutomated safety check: PassApache-2.0

Similar skills

  • Sympy

    zLanqing/codex-claude-academic-skills

    A skill your agent uses when working with symbolic mathematics in Python.

    4.6k GitHub starsUsed in 16 repos~3.4k tokens
    Research & ScienceAuto-check passed

  • Edu Analytic Geometry

    wy51ai/edulab

    把一道解析几何题解成一个自包含的交互教学网页：左栏题面 + 动态控制台（一个 可变参数滑块驱动实时重算的几何量 + 理论范围/定值指示），中栏 KaTeX 分步解析，右栏 2D Canvas 动态几何画板（椭圆/双曲线/抛物线/圆 + 动直线/动点 + 向量 + 标注 + 画笔涂鸦）。

    1.4k GitHub starsUsed in 1 repo~1.6k tokens
    Research & ScienceAuto-check passed

  • Edu Solid Geometry

    wy51ai/edulab

    把一道立体几何题解成一个自包含的交互教学网页：左侧 MathJax 分步解析， 右侧 Three.js 可交互 3D 模型（分步高亮 + 镜头切换）。支持三种入口——给定文字题目、 随机出题、上传题目图片识别后解题。覆盖正方体/长方体、棱锥/棱柱、圆柱/圆锥上的线面角、 二面角、异面直线夹角、点到平面距离、体积等题型，统一用"建系+向量法"，并由 sympy 精确 计算驱动（答案、3D…

    1.4k GitHub starsUsed in 1 repo~1.1k tokens
    Research & ScienceAuto-check passed

  • Math Tools

    ananddtyagi/cc-marketplace

    Deterministic mathematical computation using SymPy. An agent skill from ananddtyagi/cc-marketplace.

    687 GitHub starsUsed in 2 repos~1.3k tokens
    Research & ScienceAuto-check passed

  • Edu Chem Reaction

    wy51ai/edulab

    把一个化学反应做成自包含的微观 3D 交互演示网页：左/上为 Three.js 可交互分子动画 （拖滑块看断键·成键·原子重组，分步高亮），右为 KaTeX 反应方程 + 分步讲解 + 原子守恒计数 + 可选能量-反应进程曲线。支持三入口——给定文字反应/方程、随机出题、上传图片识别后演示。

    1.4k GitHub stars~1.2k tokensUpdated 10 days ago
    Research & ScienceAuto-check passed

  • Math Computation

    tradecatlabs/vibe-coding-cn

    Runs reproducible math computations and counterexample searches with SymPy, NumPy and mpmath, logging evidence without presenting results as proofs.

    17k GitHub stars~881 tokensUpdated today
    Research & ScienceAuto-check passed

More from parcadei/Continuous-Claude-v3

All 141 skills in this repo

  • Tldr Deep

    parcadei/Continuous-Claude-v3

    Full 5-layer analysis of a specific function. An agent skill from parcadei/Continuous-Claude-v3.

    3.9k GitHub starsUsed in 2 repos~677 tokens
    Auto-check passed

  • Compound Learnings

    parcadei/Continuous-Claude-v3

    Transform session learnings into permanent capabilities (skills, rules, agents).

    3.9k GitHub starsUsed in 1 repo~1.6k tokens
    Auto-check: notes

  • Gradient Methods

    parcadei/Continuous-Claude-v3

    Problem-solving strategies for gradient methods in optimization

    3.9k GitHub starsUsed in 3 repos~1k tokens
    Auto-check: notes

  • Debug Hooks

    parcadei/Continuous-Claude-v3

    Systematic hook debugging workflow. An agent skill from parcadei/Continuous-Claude-v3.

    3.9k GitHub starsUsed in 1 repo~863 tokens
    Auto-check: notes

  • Math

    parcadei/Continuous-Claude-v3

    Unified math capabilities - computation, solving, and explanation.

    3.9k GitHub starsUsed in 3 repos~1.6k tokens
    Auto-check: notes

  • Math Model Selector

    parcadei/Continuous-Claude-v3

    Routes problems to appropriate mathematical frameworks using expert heuristics

    3.9k GitHub starsUsed in 3 repos~841 tokens
    Auto-check passed

Works with

Categories

Questions about Operator Theory

What does Operator Theory do?

Problem-solving strategies for operator theory in functional analysis. Operator Theory is an agent skill from parcadei/Continuous-Claude-v3.

When should I use Operator Theory?

Operator Theory fits situations like: tasks that involve Math and symbolic computation.

How do I install Operator Theory in Claude Code?

Run `npx skills add parcadei/Continuous-Claude-v3 --skill operator-theory -a claude-code`. Or copy the skill folder (.claude/skills/math/functional-analysis/operator-theory in parcadei/Continuous-Claude-v3) into .claude/skills/operator-theory in your project. Claude Code loads it when a task matches its description.

How do I install Operator Theory in Codex?

Run `npx skills add parcadei/Continuous-Claude-v3 --skill operator-theory -a codex`. Or copy the skill folder (.claude/skills/math/functional-analysis/operator-theory in parcadei/Continuous-Claude-v3) into .agents/skills/operator-theory in your project. Codex loads it when a task matches its description.

Can I use Operator Theory in Cursor, Gemini CLI or GitHub Copilot?

Cursor, Gemini CLI, GitHub Copilot and OpenCode also load SKILL.md folders. With the skills CLI, run `npx skills add parcadei/Continuous-Claude-v3 --skill operator-theory -a cursor` (or -a gemini-cli, github-copilot or opencode for the others). To copy it by hand, put the folder in .cursor/skills/operator-theory, .gemini/skills/operator-theory, .github/skills/operator-theory and .opencode/skills/operator-theory in your project.

What does Operator Theory need to run?

Going by SKILL.md and its folder, Operator Theory needs the command-line tools its instructions call (uv). Our summary lists: Python 3. Its frontmatter pre-approves these tools: Bash, Read.

Does Operator Theory access the network?

SKILL.md contains no URLs. Its commands use uv, which can reach the network depending on how they are called. This is read from the text; nothing was executed.

Is Operator Theory safe to install?

Our automated static check of SKILL.md found notes only (pre-approves every shell command (allowed-tools: bash)), nothing it rates as a warning. It is not a guarantee. Review the folder before installing.

What licence does Operator Theory use?

Operator Theory is published under the MIT licence (the repository's licence). It allows redistribution, so the full SKILL.md is shown on this page.

How many tokens does Operator Theory use?

About 879 tokens (SKILL.md is roughly 3.5k characters). Agents keep only the skill's name and description in context until a task matches; then they load SKILL.md in full.

What are the alternatives to Operator Theory?

Skills that share tags, products or a category with Operator Theory: Sympy (zLanqing/codex-claude-academic-skills, 4.6k stars), Edu Analytic Geometry (wy51ai/edulab, 1.4k stars), Edu Solid Geometry (wy51ai/edulab, 1.4k stars) and Math Tools (ananddtyagi/cc-marketplace, 687 stars). The comparison table on this page puts their stars, adoption, token cost, safety result and licence side by side.

Who maintains Operator Theory?

parcadei (a GitHub user) maintains it in parcadei/Continuous-Claude-v3, which has 3,940 GitHub stars. The repository holds 141 skills in this directory. The repository was last updated on January 26, 2026.

Source: parcadei/Continuous-Claude-v3 on GitHub. Facts on this page come from the repository at the commit we read; the author's words are quoted as theirs.