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

Authors : Abdelaziz MAOUCHE

Pages : 9-12

Doi:10.33434/cams.627282

View : 19 | Download : 11

Publication Date : 2020-03-25

Article Type : Research Paper

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