Vol. 62, No. 2, 1976

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On the convolution algebras of H-invariant measures

John Yuan

Vol. 62 (1976), No. 2, 595–600

The totality M(eSe∕H) of bounded regular Borel measures on the orbit space eSe∕H, where S is a locally compact semigroup and H is a compact subgroup with the identity e, forms a Banach space; however, its closed subspace MH(ESe∕H) of H-invariant measures forms even a Banach algebra under a suitable convolution. Furthermore, if w is an idempotent probability measure with compact support on S, then w M(S) wwH M(S) wHNIH(eSe∕H) algebraically and in various topologies, where wH is the normalized Haar measure on some compact subgroup H.

Mathematical Subject Classification 2000
Primary: 43A10
Received: 12 May 1975
Revised: 7 October 1975
Published: 1 February 1976
John Yuan