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ArticleOriginal scientific text

Title

On a property of weak resolvents and its application to a spectral problem

Authors 1

Affiliations

  1. Department of Mathematics and Computer Science, Adam Mickiewicz University, Matejki 48/49, 60-769 Poznań, Poland

Abstract

We show that the poles of a resolvent coincide with the poles of its weak resolvent up to their orders, for operators on Hilbert space which have some cyclic properties. Using this, we show that a theorem similar to the Mlak theorem holds under milder conditions, if a given operator and its adjoint have cyclic vectors.

Keywords

ENG
weak resolvent, cyclic vector, spectral radius, Hardy class, operator model theory, scattering theory, control theory

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Annales Polonici Mathematici
1997/66/1
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Pages:
263-268
Main language of publication
English
Received
1995-11-29
Published
1997
Exact and natural sciences