F-products and nonstandard hulls for semigroups.

Derndinger [2] and Krupa [5] defined the F-product of a (strongly continuous one-parameter) semigroup (of linear operators) and presented some applications (e. g. to spectral theory of positive operators, cf. [3]). Wolff (in [7] and [8]) investigated some kind of nonstandard analogon and applied it to spectral theory of group representations. The question arises in which way these constructions are related. In this paper we show that the classical and the nonstandard F-product are isomorphic (Theorem 2.6). We also prove a little “classical” corollary (2.7.). (© 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]