Vol. 47, No. 2, 1973

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ISSN: 0030-8730
Isomorphic classes of the spaces Cσ(S)

M. A. Labbé and John Wolfe

Vol. 47 (1973), No. 2, 481–485
Abstract

Jerison introduced the Banach spaces Cσ(S) of continuous real or complex-valued odd functions with respect to an involutory homeomorphism σ : S S of the compact Hausdorff space S. It has been conjectured that any Banach space of the type Cσ(S) is isomorphic to a Eanach space of all continuous functions on some compact Hausdorff space. This conjecture is shown to be true if either (1) lS is a Cartesian product of compact metric spaces or (2) S is a linearly ordered compact Hausdorff space and σ has at most one fixed point.

Mathematical Subject Classification 2000
Primary: 46E15
Milestones
Received: 6 March 1972
Published: 1 August 1973
Authors
M. A. Labbé
John Wolfe