Commutable Matrix-Valued Functions and Operator-Valued Functions

Authors : Abdelaziz MAOUCHE

Pages : 225-235

Doi:10.33434/cams.759336

View : 19 | Download : 12

Publication Date : 2020-12-22

Article Type : Research Paper

Abstract :A simple expression is established for an analytic commutable matrix-valued function. Then a characterization of two by two functional commutative matrices is proven. Finally, a family of analytic normal compact operators on a Hilbert space, which commute with their derivatives, is shown to be functionally commutative.
Keywords : Riesz projection, Analytic matrix valued function, Commutable matrices, Eigenvalue, Holomorphic operator valued function, Resolvent, Spectrum