Isometric isomorphism of homogeneous space algebras

Tajedin Derikvand; Rajab Ali Kamyabi-Gol; Mohammad Janfada

2018/93/1-2 (9) — DOI: 10.5486/PMD.2018.8076 — pp. 125-142

Isometric isomorphism of homogeneous space algebras

Authors: Tajedin Derikvand, Rajab Ali Kamyabi-Gol and Mohammad Janfada

Abstract:

In this paper, we show that two homogeneous spaces with isometrically isomorphic algebras are topologically homeomorphic by themselves. This generalizes the well-known results of J. G. Wendel for group algebras and those of B. E. Johnson for measure algebras.

Keywords: isomorphic algebras, homogeneous spaces, strongly quasi-invariant measure, homeomorphic Hausdorff spaces

Mathematics Subject Classification: 43A15, 43A85