Vol. 47, No. 2, 1973

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Isomorphic classes of the spaces Cσ(S)

M. A. Labbé and John Wolfe

Vol. 47 (1973), No. 2, 481–485

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
Received: 6 March 1972
Published: 1 August 1973
M. A. Labbé
John Wolfe