Vol. 37, No. 1, 1971

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ISSN: 0030-8730
Multipliers and unconditional convergence of biorthogonal expansions

William Jay Davis, David William Dean and Ivan Singer

Vol. 37 (1971), No. 1, 35–39
Abstract

We solve in the affirmative a problem raised by B. S. Mityagin in 1961, namely, we prove that if (xn,fn) is a biorthogonal system for a Banach space E with (fn) total over E, such that the set of multipliers M(E,(xn,fn)) contains all sequences (𝜖i) with 𝜖i = ±1 for each i, then (xn) is an unconditional basis for E.

Mathematical Subject Classification 2000
Primary: 46B15
Milestones
Received: 3 April 1970
Published: 1 April 1971
Authors
William Jay Davis
David William Dean
Ivan Singer