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Results tagged with fa.functional-analysis
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user 124227
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
-1
votes
Flat norm metrizes the weak* topology
The statement in the text cannot possibly be correct. The spaces in question are not metrisable in the weak $\star$ topology. This is a standard fact in locally convex space theory. There are, howe …
- 102
4
votes
0
answers
117
views
Does there exist a Banach space $E$ with $L(E)$ separable?
The title says it all. Does there exist a (separable, infinite-dimensional) Banach space $E$ with the normed space $L(E)$ of bounded, linear operators thereon separable?
- 102
0
votes
Continuity and sequential continuity of a linear functional
This is indeed true and follows from the fact that your space is what is called a strict $LF$-space and the theory of the latter. This can be found in the original article by Dieudonné and Schwartz w …
- 102
2
votes
Accepted
Criteria for Minkowski functionals to induce a complete space?
There is a simple sufficient condition---that there exists a suitable locally convex topology on the space which is weaker than your norm topology and for which $K$ is complete. This is the Grothendie …
- 102
2
votes
Is $C_b(Q,E)$ linearly isometrically isomorphic to $C(\beta Q,E)$ where $\beta Q$ is the Sto...
You probably mean for the extension $F$ to be continuous. Since its image is then compact, this can only happen if the image of $f$ is relatively compact. And this condition is sufficient by the unive …
- 102