$𝒞^∞$-vectors and boundedness

• Autorzy: Jan Stochel , F. H. Szafraniec
• Języki publikacji: EN

Abstrakty

EN

The following two questions as well as their relationship are studied: (i) Is a closed linear operator in a Banach space bounded if its $𝒞^∞$-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.

Słowa kluczowe

EN

unbounded Banach space operators; boundedness of operators; paranormal operators; weighted shifts; $𝒞^∞$-vectors; bounded and analytic vectors

Kategorie tematyczne

• 47B37: Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
• 47A05: General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
• 47B25: Symmetric and selfadjoint operators (unbounded)
• 47B20: Subnormal operators, hyponormal operators, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1997
• Tom: 66
• Numer: 1
• Strony: 223-238

Daty

wydano

1997

otrzymano

1995-10-19

poprawiono

1996-05-20

Twórcy

autor

Jan Stochel

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

autor

F. H. Szafraniec

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

Bibliografia

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