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)



A characterization of the Mackey topology $ \tau(L\sp \infty, L\sp 1)$

Author: Marian Nowak
Journal: Proc. Amer. Math. Soc. 108 (1990), 683-689
MSC: Primary 46E30; Secondary 46A20
MathSciNet review: 991705
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We give a description of the Mackey topology $ \tau ({L^\infty },{L^1})$ for finite measures in terms of a family of norms defined by certain Young functions. As an application we obtain various topological characterizations of sequential convergence in $ \tau ({L^\infty },{L^1})$. Moreover, we obtain a criterion for relative weak compactness in $ {L^1}$ in terms of the integral functional defined by some Young function.

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46E30, 46A20

Retrieve articles in all journals with MSC: 46E30, 46A20

Additional Information

Keywords: Mackey topology $ \tau ({L^\infty },{L^1})$, Orlicz spaces, mixed topologies, locally solid Riesz spaces
Article copyright: © Copyright 1990 American Mathematical Society

American Mathematical Society