operator-theory
Problem-solving strategies for operator theory in functional analysis
Profile →npx skills add parcadei/Continuous-Claude-v3 --skill operator-theory --agent claude-code
Same command for any agent — swap --agent for codex, cursor, copilot.
Weekly change comes from our own snapshots, not the repository page — it measures attention, not adoption.
# 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, T*y> 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 runt
- When to Use
- Decision Tree
- Tool Commands
- Z3BoundedOperator
- SympyAdjoint
- Z3Spectral
- SympyCompact
- Key Techniques
- Cognitive Tools Reference
uv run python -m runtime.harness scripts/z3_solve.py prove "norm(Tx) <= M*norm(x)" uv run python -m runtime.harness scripts/sympy_compute.py simplify "<Tx, y> - <x, T_star_y>" uv run python -m runtime.harness scripts/z3_solve.py prove "self_adjoint implies real_spectrum" uv run python -m runtime.harness scripts/sympy_compute.py limit "norm(T - T_n)" --var n --at oo
What does the operator-theory skill do?
Problem-solving strategies for operator theory in functional analysis
How do I install it?
Run `npx skills add parcadei/Continuous-Claude-v3 --skill operator-theory --agent claude-code` — it drops the skill into your project so the agent can pick it up. Swap the --agent value for codex, cursor or copilot if you use one of those.
Where does this skill come from?
From parcadei/Continuous-Claude-v3, a repository with 3,879 stars. We read it straight from the repository tree rather than a submitted listing, so what you see here is what is actually published.
Is a popular skill a good skill?
Not necessarily. Stars measure attention, not adoption — a repository can trend for a week and be abandoned. That is why we show the weekly change from our own snapshots next to the total, instead of a single flattering number.