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>"