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ON COSINE FAMILIES CLOSE TO SCALAR COSINE FAMILIES

Part of: Groups and semigroups of linear operators, their generalizations and applications Individual linear operators as elements of algebraic systems General theory of linear operators

Published online by Cambridge University Press:  26 February 2015

WOJCIECH CHOJNACKI
WOJCIECH CHOJNACKI*
Affiliation:
School of Computer Science, The University of Adelaide, SA 5005,Australia email [email protected] Wydział Matematyczno-Przyrodniczy, Szkoła Nauk Ścisłych, Uniwersytet Kardynała Stefana Wyszyńskiego, Dewajtis 5, 01-815 Warszawa,Poland email [email protected]
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Abstract

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We prove that if two normed-algebra-valued cosine families indexed by a single Abelian group, of which one is bounded and comprised solely of scalar elements of the underlying algebra, differ in norm by less than $1$ uniformly in the parametrising index, then these families coincide.

Keywords

cosine familycosine sequencenormed algebrascalar element

MSC classification

Primary: 47D09: Operator sine and cosine functions and higher-order Cauchy problems 47C05: Operators in algebras
Secondary: 47A30: Norms (inequalities, more than one norm, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 99 , Issue 2 , October 2015 , pp. 166 - 174
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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