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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Some characterizations of the spaces $ L\sp{1}(\mu )$


Author: Kenneth L. Pothoven
Journal: Trans. Amer. Math. Soc. 162 (1971), 171-183
MSC: Primary 46.10; Secondary 18.00
DOI: https://doi.org/10.1090/S0002-9947-1971-0285894-1
MathSciNet review: 0285894
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Abstract: Answers are given to the question of when the so-called hom and tensor functors in categories of Banach spaces preserve certain short exact sequences. The answers characterize the spaces of integrable, real-valued functions $ {L^1}(\mu )$.


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DOI: https://doi.org/10.1090/S0002-9947-1971-0285894-1
Keywords: Categories of Banach spaces, pth-power integrable functions, hom functor, projective tensor product, exact sequence
Article copyright: © Copyright 1971 American Mathematical Society

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