Birnbaum-Orlicz spaces of functions on groups

Iracema M. Bund

Vol. 58 (1975), No. 2, 351–359

DOI: 10.2140/pjm.1975.58.351

Abstract

It is natural to ask how far the theory of closed invariant subspaces for L_p(G) can be extended to Birnbaum-Orlicz spaces L_A(G). If G is a compact group and A satisfles the Δ_2⁻ condition for u ≧ u₀ ≧ 0, the class of all closed invariant subspaces of L_A(G) is exactly the family {(L_A)_P : P ⊂ Σ} where Σ is the dual object of G. Distinct subsets of Σ engender distinct subspaces.

Mathematical Subject Classification 2000

Primary: 43A15

Milestones

Received: 22 February 1974

Published: 1 June 1975