finding the algebraic dimension of $\ell^p$ spaces

Asked Sep 06 '14 at 09:49

Active Sep 06 '14 at 09:52

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I want to know "how we can find the algebraic dimension(the cardinal number of the Hamel basis) for $\ell^p$ spaces." What can we say about $\ell^p(I)$, where $I$ is an infinite set?\

Moreover, for any given cardinal number $\alpha \neq \aleph_0$, is there a Banach space $X$ that its algebraic dimension equal $\alpha$?

edited Sep 06 '14 at 09:52

asked Sep 06 '14 at 09:49

Arman

see comments by to this answer – Norbert Sep 06 '14 at 10:11
I think no identity meant this answer by Andres Caicedo. (The link did not point directly to it.) – Sep 06 '14 at 17:25
See this answer https://math.stackexchange.com/questions/141535/cardinality-of-a-hamel-basis-of-ell-1-mathbbr – Chrystomath Jul 25 '20 at 09:07

finding the algebraic dimension of $\ell^p$ spaces

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