Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Quotients of Banach spaces of cotype $q$
HTML articles powered by AMS MathViewer

by Gilles Pisier PDF
Proc. Amer. Math. Soc. 85 (1982), 32-36 Request permission

Abstract:

Let $Z$ be a Banach space and let $X \subset Z$ be a $B$-convex subspace (equivalently, assume that $X$ does not contain $l_1^n$’s uniformly). Then every Bernoulli series $\Sigma _{n = 1}^\infty {\varepsilon _n}{z_n}$ which converges almost surely in the quotient $Z/X$ can be lifted to a Bernoulli series a.s. convergent in $Z$. As a corollary, if $Z$ is of cotype $q$, then $Z/X$ is also of cotype $q$. This extends a result of [4] concerning the particular case $Z = {L_1}$.
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46B20, 28C20, 60B11
  • Retrieve articles in all journals with MSC: 46B20, 28C20, 60B11
Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 85 (1982), 32-36
  • MSC: Primary 46B20; Secondary 28C20, 60B11
  • DOI: https://doi.org/10.1090/S0002-9939-1982-0647892-8
  • MathSciNet review: 647892