Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 

 

Topological equivalence in the space of integrable vector-valued functions


Author: Semion Gutman
Journal: Proc. Amer. Math. Soc. 93 (1985), 40-42
MSC: Primary 46E40; Secondary 28B05
DOI: https://doi.org/10.1090/S0002-9939-1985-0766523-2
MathSciNet review: 766523
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The Banach space $ {L^1}(0,T;X)$ is retopologized by $ \vert\vert\vert f\vert\vert\vert = \max\vert\vert\int _a^bfdt\vert\vert$, $ 0 \leqslant a \leqslant b \leqslant T$, where $ \vert\vert.\vert\vert$ is the norm in the given Banach space $ X$. It is shown here that this topology coincides with the usual weak topology of $ {L^1}(0,T;X)$ on a wide class of weakly compact subsets.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46E40, 28B05

Retrieve articles in all journals with MSC: 46E40, 28B05


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1985-0766523-2
Keywords: Vector-valued functions, weak compactness, Banach spaces, topological equivalence
Article copyright: © Copyright 1985 American Mathematical Society