Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with banach-spaces
Search options not deleted
user 272040
A Banach space is a complete normed vector space: A vector space equipped with a norm such that every Cauchy sequence converges.
14
votes
What standard Banach space is isomorphic to the completion of this different normed structur...
In what follows I will show that the closure of $\ell^1$ under the norm $|x|=\int_1^2|x|_pdp$ is nothing but the Orlicz space $L_\Phi$, where $\Phi$ is the function
$$\Phi(t)=\frac{t^2-|t|}{\ln|t|}$$
…
- 1,065
6
votes
1
answer
272
views
Analytic maps on Banach spaces: analyticity upgrade
Consider the following problem.
Let $E,F,G$ be real or complex Banach spaces, such that $F\subset G$ with continuous embedding. Let $U\subset E$ an open set and
$$ f:U\to G $$
an analytic map, such th …
- 1,065
3
votes
Analytic maps on Banach spaces: analyticity upgrade
I will summarize what has been said in the comments (thanks to Jochen Glueck for all his help).
The answer to the question is no, in general. What is going on is actually very simple.
Theorem. Let $E, …
- 1,065