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Proceedings of the American Mathematical Society

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

 

 

Subspaces of $ L\sb {p,q}$


Authors: N. L. Carothers and S. J. Dilworth
Journal: Proc. Amer. Math. Soc. 104 (1988), 537-545
MSC: Primary 46E30; Secondary 46B20
MathSciNet review: 962825
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Abstract: We examine the subspace structure of the Lorentz function space $ {L_{p,q}}[0,\infty )$. Our main result is that a subspace of $ {L_{p,q}}[0,\infty ),p \ne 2,q < \infty $, must either strongly embed in $ {L_p}[0,1]$ or contain a complemented copy of $ {l_q}$.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0962825-8
Keywords: Lorentz function spaces, subspaces
Article copyright: © Copyright 1988 American Mathematical Society