BANACH ALGEBRA STRUCTURE IN FOURIER SPACES AND GENERALIZATION OF HARMONIC-ANALYSIS ON LOCALLY COMPACT GROUPS

Let (M, G, α) be a continuous W*-dynamical system. Then, the predual (G⨂αM)* of the crossed product G⨂αM of M by G can be turned into a Banach algebra and some of the notions and theorems in harmonic analysis on locally compact groups are extended to the corresponding ones in the crossed products. Among others, one can get a criterion for T in G⨂αM to fall in M: T=πα (x) for some x≠0 in M if and only if the support of T reduces to the unit e in G. © 1979, Mathematical Society of Japan. All Rights Reserved.