Analytic Families of Self-Adjoint Compact Operators Which Commute with Their Derivative

Abstract

Spectral properties of analytic families of compact operators on a Hilbert space are studied. The results obtained are then used to establish that an analytic family of self-adjoint compact operators on a Hilbert space $\mathcal{H},$ which commute with their derivative, must be functionally commutative.

Keywords

• compact operator
• spectral decomposition
• analytic projection
• functional commutativity