| Title:
|
Absolutely summing operators on the Banach space of totally measurable functions (English) |
| Author:
|
Nowak, Marian |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0011-4642 |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
151 |
| Issue:
|
3 |
| Year:
|
2026 |
| Pages:
|
377-384 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $\Sigma $ be a $\sigma $-algebra of subsets of a set $\Omega $, and $X$ and $Y$ be Banach spaces. Let $B(\Sigma ,X)$ stand for the Banach space of all $X$-valued totally measurable functions on $\Omega $, equipped with the supremum norm. We study absolutely summing operators ${T\colon B(\Sigma ,X)\rightarrow Y}$. We characterize absolutely summing operators $T\colon B(\Sigma ,X)\rightarrow Y$ in terms of their representing operator-valued measures. It is shown that the classes of dominated operators and absolutely summing operators $T\colon B(\Sigma ,X)\rightarrow Y$ coincide if and only if every bounded linear operator $U\colon X\rightarrow Y$ is absolutely summing. (English) |
| Keyword:
|
space of totally measurable functions |
| Keyword:
|
dominated operator |
| Keyword:
|
absolutely summing operator |
| Keyword:
|
operator-valued measure |
| MSC:
|
46G10 |
| MSC:
|
47B10 |
| DOI:
|
10.21136/MB.2025.0153-24 |
| . |
| Date available:
|
2026-08-24T07:50:24Z |
| Last updated:
|
2026-08-24 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153712 |
| . |
| Reference:
|
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