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Results tagged with banach-spaces
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user 148734
A Banach space is a complete normed vector space: A vector space equipped with a norm such that every Cauchy sequence converges.
4
votes
1
answer
136
views
Are unit balls in Banach spaces retracts of bidual balls?
Let $X$ be a separable Banach space embedded canonically in $X^{**}$. Is there a retraction from the unit ball $B_{X^{**}}$ of $X^{**}$ onto the unit ball $B_X$ of $X$?
When we insist on uniformly co …
- 97
4
votes
1
answer
361
views
Approximation property of a Banach space in terms of finite-rank projections
Let $X$ be a separable Banach space. Is this property equivalent to the approximation property?
There exists a chain $X_n$ of finite-dimensional subspaces of $X$, each being a range of some projectio …
- 97
1
vote
1
answer
192
views
Strictly increasing functions in reflexive subspaces of $C([0,1])$
By the Banach-Mazur theorem, every separable Banach space $X$ embeds into $C([0,1])$. When $X$ is reflexive, it is not possible to find a sequence of disjointly supported, non-negative functions in an …
- 97