Spectral mapping theorems for exponentially bounded C-semigroups in Banach spaces
type: Item
instance of: scholarly article
title: Spectral mapping theorems for exponentially bounded C-semigroups in Banach spaces
zbMATH Open document ID: 0683.47028
DOI: 10.1007/BF02573232
author: Ki Sik Ha
published in: Semigroup Forum
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/134955
review text: Let X be a Banach space and C an injective bounded linear operator on X, with dense range. A strongly continuous family \(\{S_ t\}_{t\geq 0}\) of bounded linear operators on X is called an exponentially bounded C- semigroup if (i) \(S_ 0=C;\) (ii) \(S_{s+t}C=S_ sS_ t\) whenever s,t\(\geq 0;\) (iii) \(\| S_ t\| \leq M \exp (at)\) for suitable nonnegative numbers M and a and any \(t\geq 0.\) In the present paper the author proves a spectral mapping theorem for such semigroups.
Mathematics Subject Classification ID: 47D03
zbMATH DE Number: 4119043
zbMATH Keywords: exponentially bounded C-semigroup
zbMATH Keywords: spectral mapping theorem
MaRDI profile type: Publication
cites work: The Cauchy Problem and a Generalization of the Hille-Yosida Theorem
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cites work: On the generators of exponentially bounded C-semigroups
cites work: Exponentially bounded C-semigroups and generation of semigroups
cites work: Semigroups of linear operators and applications to partial differential equations
cites work: On the exponentially bounded C-semigroups
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description: scientific article; zbMATH DE number 4119043