# ${}^{\infty}$-vectors and boundedness

Annales Polonici Mathematici (1997)

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

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topJan 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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