Multipliers and unconditional convergence of biorthogonal expansions

William Jay Davis, David William Dean and Ivan Singer

Vol. 37 (1971), No. 1, 35–39

DOI: 10.2140/pjm.1971.37.35

Abstract

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

Mathematical Subject Classification 2000

Primary: 46B15

Milestones

Received: 3 April 1970

Published: 1 April 1971