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ArticleOriginal scientific text

Title

^∞-vectors and boundedness

Authors 1, 1

Affiliations

  1. Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland

Abstract

The following two questions as well as their relationship are studied: (i) Is a closed linear operator in a Banach space bounded if its ^∞-vectors coincide with analytic (or semianalytic) ones? (ii) When are the domains of two successive powers of the operator in question equal? The affirmative answer to the first question is established in case of paranormal operators. All these investigations are illustrated in the context of weighted shifts.

Keywords

ENG
^∞-vectors, ^∞-vectors, ^∞-vectors, ^∞-vectors, ^∞-vectors, ^∞-vectors

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Annales Polonici Mathematici
1997/66/1
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Pages:
223-238
Main language of publication
English
Received
1995-10-19
Accepted
1996-05-20
Published
1997
Exact and natural sciences