A note on semigroups of operators on a locally convex space

Autor:	K. Singbal-Vedak
Rok vydání:	1965
Předmět:	Combinatorics Discrete mathematics Semigroup Applied Mathematics General Mathematics Banach space Convex set Special classes of semigroups Convex body Convex cone Operator theory Choquet theory Mathematics
Zdroj:	Proceedings of the American Mathematical Society. 16:696-702
ISSN:	1088-6826 0002-9939
Popis:	1. The object of this note is to generalize certai'i results in the theory of semigroups of continuous linear operators on a Banach space to the case where, instead of a Banach space, we consider a locally convex space. A family { T(t) }'>o of linear operators on a vector space is called a semigroup if T(t+??) = T(t) o T(-q), #, 7(0, oo). E. Hille [4] and N. Dunford [2] have proved that if { T() } >o is a semigroup of bounded linear operators on a Banach space E such that for every xCE, t-?T(t)x is a measurable function from (0, oo) into E and such that || T(t)1f5 0(8 T(t)x is a continuous function from (0, oo) into E for xEE. Proposition 2 is an analogue of this result while Propositions 3 and 4 are analogues of results due to R. S. Phillips [51 and P. Lax, respectively.
Databáze:	OpenAIRE
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