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(1966)
H o f m a n n and P. S. M o s t e r t
K. Urbanik (1972)
Lévy's probability measures on Euclidean spacesStudia Mathematica, 44
K. Urbanik (1978)
Lévy's probability measures on Banach spacesStudia Mathematica, 63
DEMONSTRATIO MATHEMATICAVol. XXXIVNo 22001Bohdan MincerTHE EXISTENCE OF ONE-PARAMETER SEMIGROUPSAND CHARACTERIZATIONSOF OPERATOR-LIMIT DISTRIBUTIONSDedicated to Professor Kazimierz Urbanikin honour of fiftieth anniversaryof his work at Wroclaw University1. Throughout this paper we shall work with a Banach space X with thenorm || • ||. We write B(X) for the algebra of continuous linear operatorson X with the norm topology. By a semigroup we mean a subsemigroup ofB(X) under the composition operation.In the theory of operator-limit distributions some compact semigroupsassociated with probability measures play a very essential role. Furthermore,it is a great importance whether there exist one-parameter semigroups insemigroups in question (cf., e.g.,[2]). The existence of one parameter semigroups was intensively investigated in the theory of compact semigroups (cf.,e.g., [1] Chapter B, Section 3). The results proved there are concentrated onpurely topological semigroups problems. Moreover, it seems rather complicated to apply these results in the probability on Banach spaces setting. Inthe paper we give a construction of one-parameter semigroups in some compact semigroups of B(X). The result could be applied directly to a problemoccuring in the theory of operator-limit distributions.2. Given a subset A of B{X), by Sem(A) we shall denote the closed subsemigroup of B{X) spanned by A. By a projector we
Demonstratio Mathematica – de Gruyter
Published: Apr 1, 2001
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