Original scientific paper

A note on compact operators and operator matrices

D. Bakić
B. Guljaš

Abstract

In this note two properties of compact operators acting on a separable Hilbert space are discussed. In the first part
a characterization of compact operators is obtained for
bounded operators represented as tri-block diagonal matrices with finite blocks. It is also proved that one can obtain such a tri-block diagonal matrix representation for each bounded operator starting from any orthonormal basis of the underlying Hilbert space by an arbitrary small Hilbert-Schmidt perturbation.
The second part is devoted to the so-called Hummel's property of compact operators: each compact operator has a uniformly small orthonormal basis for the underlying Hilbert space. The class of all bounded operators satisfying Hummel's condition is determined.

Keywords

compact operator; orthonormal basis

Hrčak ID:

869

URI

https://hrcak.srce.hr/869

Publication date:

11.12.1999.

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