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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Linear maps do not preserve countable dimensionality


Authors: Mladen Bestvina and Jerzy Mogilski
Journal: Proc. Amer. Math. Soc. 93 (1985), 661-666
MSC: Primary 46B99; Secondary 54F45
MathSciNet review: 776199
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Abstract: Examples of linear maps between normed spaces are constructed, including a one-to-one map from a countable-dimensional linear subspace of $ {l_2}$ onto $ {l_2}$. We prove that the linear span of a countable-dimensional linearly independent subset of a normed linear space is, in many cases, countable dimensional.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0776199-6
PII: S 0002-9939(1985)0776199-6
Keywords: Countable dimension, normed linear spaces, continuous linear maps, Hamel basis, linear span, embeddings onto linearly independent sets
Article copyright: © Copyright 1985 American Mathematical Society