Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


An alternating procedure for operators on $ L\sb p$ spaces

Authors: M. A. Akcoglu and L. Sucheston
Journal: Proc. Amer. Math. Soc. 99 (1987), 555-558
MSC: Primary 47A35; Secondary 28D99, 47B38
MathSciNet review: 875396
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ {L_p}$ be the usual Banach spaces over a $ \sigma $-finite measure space. If $ 1{\text{ < }}p{\text{ < }}\infty $ and $ q = p{(p - 1)^{ - 1}}$, then $ {\psi _p}:{L_p} \to {L_q}$ denotes the duality mapping defined by the requirements that $ (f,{\psi _p}f) = \left\Vert f \right\Vert _p^p = {\left\Vert f \right\Vert _p}\left\Vert {{\psi _p}f} \right\Vert q,f \in {L_p}$. If $ T:{L_p} \to {L_p}$ is a bounded linear operator, then $ M(T):{L_p} \to {L_p}$ is the mapping defined by $ M(T) = {\psi _q}{T^ * }{\psi _p}T$, where $ {T^ * }:{L_q} \to {L_q}$ is the adjoint of $ T$. It is proved that if $ {T_n}$ is a sequence of operators on $ {L_p}$ such that $ \left\Vert {{T_n}} \right\Vert \leq 1$ for all $ n$, then $ M({T_n} \cdots {T_2}{T_1})f$ converges in $ {L_p}$ for all $ f \in {L_p}$.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47A35, 28D99, 47B38

Retrieve articles in all journals with MSC: 47A35, 28D99, 47B38

Additional Information

PII: S 0002-9939(1987)0875396-0
Keywords: Duality map on $ {L_p}$, contractions on $ {L_p}$
Article copyright: © Copyright 1987 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia