|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'501'711
Articles rated: 2609
19 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
The Bartle-Dunford-Schwartz and the Dinculeanu-Singer theorems revisited | | Fernando Muñoz
; Eve Oja
; Cándido Piñeiro
; | | Date: |
21 Dec 2016 | | Abstract: | Let $X$ and $Y$ be Banach spaces and let $Omega$ be a compact Hausdorff
space. Denote by $mathcal{C}_{p}(Omega,X)$ the space of $p$-continous
$X$-valued functions, $1leq pleq infty$. For operators
$Sinmathcal{L}(mathcal{C}(Omega),mathcal{L}(X,Y))$ and
$Uinmathcal{L}(mathcal{C}_{p}(Omega,X),Y)$, we establish integral
representation theorems with respect to a vector measure $m:Sigma
ightarrow
mathcal{L}(X,Y^{**})$, where $Sigma$ denotes the $sigma$-algebra of Borel
subsets of $Omega$. The first theorem extends the classical
Bartle-Dunford-Schwartz representation theorem. It is used to prove the second
theorem, which extends the classical Dinculeanu-Singer representation theorem,
also providing to it an alternative simpler proof. For the latter (and the
main) result, we build the needed integration theory, relying on a new concept
of the $q$-semivariation, $1leq qleq infty$, of a vector measure
$m:Sigma
ightarrow mathcal{L}(X,Y^{**})$. | | Source: | arXiv, 1612.7312 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER