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Convergence Theorems for Semi-Groups of Linear Operators of Class (1,A).
Technical summary rept.,
WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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The subject of approximation of semi-groups of operators has been studied by a many authors under the assumption that the sequence of semi-groups Tnt is uniformly bounded for all values of the parameter in the sense that T sub nt or M, where M is independent of n and t. In particular this has restricted the results to semi-groups of class sub o. The purpose of this paper is to investigate this problem for a more general class of semi-groups, namely the class 1,A and thereby generalize some results of Trotter, Kurtz and Kato. Keywords Banach space.
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