Vol. 60, No. 2, 1975

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Monotone bases in Lp

Leonard Eliezer Dor and Edward Wilfred Odell, Jr.

Vol. 60 (1975), No. 2, 51–61
Abstract

We prove that every monotone basis (decomposition) for Lp(μ), 1 < p < , is unconditional. The structure of such bases is closely related to that of the usual Haar basis. This structure is described here, and it is shown that there is an uncountable number of mutually non-equivalent monotone bases for Lp. The structure of monotone bases in L1 is also considered, and the equivalence question there is characterized in analytic terms.

Mathematical Subject Classification 2000
Primary: 46E30
Milestones
Received: 17 July 1974
Published: 1 October 1975
Authors
Leonard Eliezer Dor
Edward Wilfred Odell, Jr.