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Brief communications

On a Class of Completely Continuous Operators in Hilbert Spaces

G. M. Gubreev, G. V. Lukashenko

Poltava National Technical University named after Yuri Kondratyuk

Abstract: We introduce a class $G$ of completely continuous operators and prove theorems on the spectral structure of these operators. In particular, operators of this class are similar to model operators in de Branges spaces.

Keywords: de Branges space, similarity of operators, unconditional basis.

UDC: 517.98

Received: 28.03.2008

DOI: 10.4213/faa2956

 English version: Functional Analysis and Its Applications, 2009, 43:2, 143–146

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