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operator-theory

Solve operator theory problems using Z3 proofs and SymPy symbolic computation.

8|1|Updated Jan 4, 2026
Search Tags:#functional analysis#spectral theory#operator theory#bounded operators#adjoint operators#compact operators
One-click install
npx skills add https://github.com/scooter-lacroix/Maestro --skill operator-theory
Or copy as Structured Prompt for Agent▼
Please help me install this Agent Skill.
Skill: operator-theory
Source: https://github.com/scooter-lacroix/Maestro/tree/main/maestro/skills/math/math/functional-analysis/operator-theory
Command: npx skills add https://github.com/scooter-lacroix/Maestro --skill operator-theory

SYSTEM DOCUMENTATION & REQUIREMENTS

💡 This Skill requires z3-solver, sympy, and includes scripts (resource) and references (resource) components.

What problem does it solve?

This Skill provides strategies and tools for solving problems related to operator theory within the field of functional analysis.

Core Features & Use Cases

  • Bounded Operator Verification: Check if an operator T satisfies ||Tx|| <= M||x||.
  • Adjoint Operator Computation: Define and compute the adjoint operator T*.
  • Spectral Theory Analysis: Analyze the spectrum of operators, especially for self-adjoint operators.
  • Compact Operator Identification: Understand and work with compact operators and their properties.
  • Use Case: When faced with a complex operator in a functional analysis problem, use this skill to verify its boundedness or compute its spectral properties.

Quick Start

Use the operator-theory skill to prove that a self-adjoint operator has a real spectrum.

Frequently Asked Questions about operator-theory

High-intent search queries and answers about installing and using this skill.

FAQPage Schema
How do I verify if a bounded operator satisfies the norm inequality in functional analysis?▼

Bounded operator verification checks if an operator T satisfies the inequality ||Tx|| <= M||x|| for a constant M. This Skill uses symbolic computation to evaluate and confirm boundedness properties for operators in functional analysis.

How do I compute the adjoint operator for a given operator in functional analysis?▼

Computing the adjoint operator involves defining and calculating the operator T* for a given operator T. This Skill provides methods to compute adjoint operators using symbolic computation tools to handle the mathematical definitions.

Can I use Z3 to prove that a self-adjoint operator has a real spectrum?▼

Yes, Z3 is utilized for proofs in this Skill, including proving that self-adjoint operators have real spectra. Spectral theory analysis examines the spectrum of operators with Z3 handling the formal proof verification.

How do I identify compact operators and work with their properties?▼

Compact operator identification involves understanding and working with operators that map bounded sets to relatively compact sets. This Skill provides tools to identify compact operators and analyze their properties within functional analysis.

Does this operator theory tool require SymPy for spectral theory analysis?▼

Yes, SymPy is a required dependency for symbolic computation in this Skill. It is used alongside Z3-solver to perform spectral theory analysis, verify bounded operators, and compute adjoint operators.

What is the best way to analyze spectral properties of operators in functional analysis?▼

The best way to analyze spectral properties is using this Skill's spectral theory analysis capabilities, which examine operator spectra with a focus on self-adjoint operators. It leverages Z3 for proofs and SymPy for symbolic computation.

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