| Title:
|
Compact operators and integral equations in the $\cal {HK}$ space (English) |
| Author:
|
Boonpogkrong, Varayu |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
72 |
| Issue:
|
1 |
| Year:
|
2022 |
| Pages:
|
239-257 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The space $\mathcal {HK}$ of Henstock-Kurzweil integrable functions on $[a,b]$ is the uncountable union of Fréchet spaces $\mathcal {HK}(X)$. In this paper, on each Fréchet space $\mathcal {HK}(X)$, an $F$-norm is defined for a continuous linear operator. Hence, many important results in functional analysis, like the Banach-Steinhaus theorem, the open mapping theorem and the closed graph theorem, hold for the $\mathcal {HK}(X)$ space. It is known that every control-convergent sequence in the $\mathcal {HK}$ space always belongs to a $\mathcal {HK}(X)$ space for some $X$. We illustrate how to apply results for Fréchet spaces $\mathcal {HK}(X)$ to control-convergent sequences in the $\mathcal {HK}$ space. Examples of compact linear operators are given. Existence of solutions to linear and Hammerstein integral equations is proved. (English) |
| Keyword:
|
compact operator |
| Keyword:
|
integral equation |
| Keyword:
|
controlled convergence |
| Keyword:
|
Henstock-Kurzweil integral |
| MSC:
|
26A39 |
| MSC:
|
26A42 |
| idZBL:
|
Zbl 07511564 |
| idMR:
|
MR4389117 |
| DOI:
|
10.21136/CMJ.2021.0447-20 |
| . |
| Date available:
|
2022-03-25T08:31:36Z |
| Last updated:
|
2024-04-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/149584 |
| . |
| Reference:
|
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