∞ -vectors and boundedness

Jan Stochel; F. H. Szafraniec

Annales Polonici Mathematici (1997)

  • Volume: 66, Issue: 1, page 223-238
  • ISSN: 0066-2216

Abstract

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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.

How to cite

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Jan Stochel, and F. H. Szafraniec. "$^∞$-vectors and boundedness." Annales Polonici Mathematici 66.1 (1997): 223-238. <http://eudml.org/doc/270026>.

@article{JanStochel1997,
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.},
author = {Jan Stochel, F. H. Szafraniec},
journal = {Annales Polonici Mathematici},
keywords = {unbounded Banach space operators; boundedness of operators; paranormal operators; weighted shifts; $^∞$-vectors; bounded and analytic vectors; closed linear operator; -vectors},
language = {eng},
number = {1},
pages = {223-238},
title = {$^∞$-vectors and boundedness},
url = {http://eudml.org/doc/270026},
volume = {66},
year = {1997},
}

TY - JOUR
AU - Jan Stochel
AU - F. H. Szafraniec
TI - $^∞$-vectors and boundedness
JO - Annales Polonici Mathematici
PY - 1997
VL - 66
IS - 1
SP - 223
EP - 238
AB - 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.
LA - eng
KW - unbounded Banach space operators; boundedness of operators; paranormal operators; weighted shifts; $^∞$-vectors; bounded and analytic vectors; closed linear operator; -vectors
UR - http://eudml.org/doc/270026
ER -

References

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