Vol. 25, No. 3, 1968

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Linear functionals on Orlicz spaces: General theory

Malempati Madhusudana Rao

Vol. 25 (1968), No. 3, 553–585

Let Φ be a generalized Young’s function and LΦ the corresponding Orlicz space, on a general measure space. The problem considered here is the characterization of the dual space (LΦ), in terms of integral representations, without any further restrictions. A complete solution of the problem is presented in this paper. If Φ is continuous and the measure space is sigma finite (or localizable), then a characterization of the second dual (LΦ)∗∗ is also given. A detailed account of the quotient spaces of LΦ relative to certain subspaces is presented; and the analysis appears useful in the study of such spaces as the Riesz and Köthe-Toeplitz spaces.

Mathematical Subject Classification 2000
Primary: 46E30
Received: 7 February 1967
Published: 1 June 1968
Malempati Madhusudana Rao