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Proceedings of the American Mathematical Society

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

 

 

Hereditary completeness and quasi-reflexivity


Author: T. K. Mukherjee
Journal: Proc. Amer. Math. Soc. 46 (1974), 285-286
MSC: Primary 46B10
DOI: https://doi.org/10.1090/S0002-9939-1974-0352944-1
MathSciNet review: 0352944
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Abstract: In this note, we prove that the countable direct sum of quasi-reflexive Banach spaces is hereditarily complete and hence the separated countable inductive limit of quasi-reflexive Banach spaces is complete.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0352944-1
Keywords: Quasi-reflexive, barreled space, countable-codimensional subspace
Article copyright: © Copyright 1974 American Mathematical Society