Linear maps do not preserve countable dimensionality
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- by Mladen Bestvina and Jerzy Mogilski PDF
- Proc. Amer. Math. Soc. 93 (1985), 661-666 Request permission
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.References
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Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 93 (1985), 661-666
- MSC: Primary 46B99; Secondary 54F45
- DOI: https://doi.org/10.1090/S0002-9939-1985-0776199-6
- MathSciNet review: 776199