Naslov
A note on compact operators and operator matrices

Autori
Bakić, Damir ; Guljaš, Boris

Izvornik
Mathematical communications (Osijek) (1331-0623) 4 (1999), 1; 159-165

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
compact operator; orthonormal basis

Sažetak
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 a 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 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.}

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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