On a Class of Completely Continuous Operators in Hilbert Spaces
Funkcionalʹnyj analiz i ego priloženiâ, Tome 43 (2009) no. 2, pp. 75-79.

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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.
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G. M. Gubreev; G. V. Lukashenko. On a Class of Completely Continuous Operators in Hilbert Spaces. Funkcionalʹnyj analiz i ego priloženiâ, Tome 43 (2009) no. 2, pp. 75-79. http://geodesic.mathdoc.fr/item/FAA_2009_43_2_a6/

[1] K. Gofman, Banakhovy prostranstva analiticheskikh funktsii, IL, M., 1963

[2] L. de Branges, Hilbert Spaces of Entire Functions, Prentice-Hall, 1968 | MR | Zbl

[3] Dzh. Garnett, Ogranichennye analiticheskie funktsii, Mir, M., 1984 | MR

[4] G. M. Gubreev, Algebra i analiz, 12:6 (2000), 1–97 | MR

[5] G. M. Gubreev, A. A. Tarasenko, Funkts. analiz i ego pril., 40:1 (2006), 71–75 | DOI | MR | Zbl

[6] M. M. Malamud, Trudy MMO, 60, 1999, 199–259 | MR