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UNBOUNDED 2-HYPEREXPANSIVE OPERATORS

Published online by Cambridge University Press:  20 January 2009

Zenon J. Jabłonski  and
Jan Stochel
Zenon J. Jabłonski
Affiliation:
Instytut Matematyki, Uniwersytet Jagiellonski, ul. Reymonta 4, PL-30059, Kraków, Poland (jablonsk@im.uj.edu.pl; stochel@im.uj.edu.pl)
Jan Stochel
Affiliation:
Instytut Matematyki, Uniwersytet Jagiellonski, ul. Reymonta 4, PL-30059, Kraków, Poland (jablonsk@im.uj.edu.pl; stochel@im.uj.edu.pl)
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Abstract

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It is shown that most properties of (bounded) completely hyperexpansive operators remain valid for unbounded $2$-hyperexpansive operators. Powers of closed $2$-hyperexpansive operators are proved to be closed and $2$-hyperexpansive. Various parts of spectra of such operators are calculated. $2$-hyperexpansive weighted shifts are investigated. Examples of unbounded closed $2$-hyperexpansive ($2$-isometric) operators with invariant dense domains are established.

AMS 2000 Mathematics subject classification: Primary 47A05; 47B37. Secondary 47B20; 47B10

Keywords

unbounded operatorsclosedness of powers of operators2-hyperexpansive operators2-isometriesparanormal operatorsweighted shifts
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 44 , Issue 3 , October 2001 , pp. 613 - 629
Copyright
Copyright © Edinburgh Mathematical Society 2001