ON THE SPECTRUM OF A MORPHISM OF QUOTIENT HILBERT SPACES

Surveys in Mathematics and its Applications

ISSN 1842-6298
Volume 1 (2006), 13 - 22

ON THE SPECTRUM OF A MORPHISM OF QUOTIENT HILBERT SPACES

Sorin Nădăban

Abstract. In this paper we define the notion of spectrum for a morphism of quotient Hilbert spaces. The definition is the same with the one given by L.Waelbroeck but the proofs that the spectrum is a compact and nonempty set are different. In this context we also make some remarks concerning the resolvent function and the spectral radius.

2000 Mathematics Subject Classification: 47A10, 46M18.
Keywords: quotient Hilbert spaces, morphism, spectrum.

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References

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Sorin Năbădan
Department of Mathematics, Faculty of Exact Sciences,
University "Aurel Vlaicu" of Arad, Romania.
e-mail: snadaban@gmail.com

http://www.utgjiu.ro/math/sma