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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Integral operators and the compactness of induced representations


Authors: Robert C. Busby, Irwin Schochetman and Harvey A. Smith
Journal: Trans. Amer. Math. Soc. 164 (1972), 461-477
MSC: Primary 46J99; Secondary 47G05
MathSciNet review: 0295099
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Abstract: Integral operators are investigated which are compositions of multiplication by bounded vector valued functions and convolutions with vector valued functions. All of the functions are based on a fixed locally compact group. Conditions are given under which certain of these operators are compact. As an application of these conditions we consider induced representations of twisted group algebras (these are generalizations of representations of groups induced from closed normal sub-groups in the sense of Mackey and include these as special cases) and we give necessary and sufficient conditions for these representations to be compact (that is, to consist entirely of compact operators).


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DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0295099-7
PII: S 0002-9947(1972)0295099-7
Keywords: Compact integral operator, C.C.R. representation, induced representation, twisted group algebra, covariance algebra
Article copyright: © Copyright 1972 American Mathematical Society