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Results tagged with fa.functional-analysis
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user 8250
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
3
votes
Accepted
Cesaro means for $\alpha<1$ and Banach limits
The paper G.G. Lorentz: A contribution to the theory of divergent sequences; Acta mathematica, Volume 80, Number 1, 1960, 167-190; DOI: 10.1007/BF02393648, contains several interesting results relate …
- 4,713
6
votes
Accepted
Reference on the countable product of Banach spaces
I am posting a CW answer. Feel free to add other references.
Here are some references containing at least some basic facts about the construction from the question (or at least the fact that it yield …
29
votes
Accepted
Dual space of $\ell^\infty$
Obviously, the OP intended to ask about this sentence
"$f\in\ell_\infty^*$ is the sum of an element of $\ell_1$ and an element null on $c_0$"
from the paper D. H. Fremlin and M. Talagrand: A Gaussian …
- 4,713
4
votes
Accepted
What is a generalized limit?
I tried to search for renault ideal "generalized limit" to see whether I will find some related works where the definition of this notion is included.
I found this thesis: Groupoid Crossed Products …
- 4,713
9
votes
Accepted
Do multiplicative Banach limits exist?
I do not think that this is the usual definition of Banach limit. (What I know under this name is linear functional on $l_\infty$ which is positive, shift-invariant and extends the usual limit, see th …
- 4,713
11
votes
Accepted
Density-$c_0$ in $\ell^\infty$
This type of convergence is often called statistical convergence.
The paper Constantin P. Niculescu, Gabriel T. Prajitura: Some open problems concerning the convergence of positive series
(arXiv:1201 …
- 4,713
3
votes
relation between of uniformly rotund in every direction and uniformly rotund and locally uni...
I will copy here an exercise from Megginson's book An Introduction to Banach Space Theory, since I think it answers at least partially your question.
For definitions on some notions (and also for som …
2
votes
Ideal characterization of almost convergence
A slightly different argument using the sequence $x=(1,0,1,0,1,0,\dots)$.$\newcommand{\I}{\mathcal I}\newcommand{\Ilim}{\operatorname{\I-lim}}\newcommand{\Flim}{\operatorname{\mathcal F-lim}}\newcomma …
- 4,713