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Results tagged with fa.functional-analysis
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user 16537
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
2
votes
2
answers
1k
views
Sufficient conditions to the existence of a weakly convergent subsequence from a Cauchy sequ...
Bonsoir/bonjour à toutes et à tous.
The title has it all, but... We know (as a consequence of the Eberlein-Šmulian theorem) that any bounded sequence, $\{x_n\}_{n \;\! \in \;\! \mathbb{N}}$, in a (re …
- 10.5k
4
votes
0
answers
1k
views
Applications of Riesz's lemma for the unit ball
I should give a talk on something I'm working on, and I'd like to have a list, as complete as possible, of applications, in and out of functional analysis, of the following classical result by F. Ries …
- 10.5k
5
votes
3
answers
903
views
References for "different" proofs of the spectral theorem for compact operators
It is with some sort of reverential fear that I've come here to write. I've been reading you for a long time, but writing is another story... In any case, I suppose it is too late now to back out!
Th …
- 10.5k
1
vote
1
answer
382
views
All and the only algebraically closed fields s.t. any regular n-by-n matrix has a k-th root ...
The title has it all. I'm looking for a proof/disproof of the fact that an algebraically closed field, say $\mathbb K$, has characteristic zero iff the following property (R) holds: For all $n,k \in \ …
- 10.5k
9
votes
3
answers
2k
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Generalizations and relative applications of Fekete's subadditive lemma
Fekete's (subadditive) lemma takes its name from a 1923 paper by the Hungarian mathematician Michael Fekete [1]. A historical overview and references to (a couple of) generalizations and applications …
- 10.5k
2
votes
1
answer
346
views
The point of view of semicats in functional analysis
I'm completing a paper about (Mitchell's) semicats (well, not exactly, but let's say so for simplicity), and as a motivational example I'd like to mention at some point that the monic/epic morphisms o …
- 10.5k
2
votes
Reference for a strong intermediate value theorem for measures
It is also a special case of Theorem 15 (p. 43) in:
A. Fryszkowski, Fixed Point Theory for Decomposable Sets, Topological Fixed Point Theory and Its Applications 2, Dordrecht: Kluwer Academic Publ …
- 10.5k
0
votes
Terminology: Banach spaces equipped with continuous associative product?
To my knowledge, something in the same vein was first (?) considered in: C. Le Page (1967), Sur quelques conditions impliquant la commutativité dans les algèbres de Banach, C.R.A.S. Paris, Ser. A-B, 2 …
0
votes
1
answer
303
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Embedding a semigroup into a divisible semigroup
The following is motivated by the fact that I'd like to have a way, much better if canonical, to isometrically embed a normed group into a normed divisible group. But semigroups are a much more natura …
- 10.5k