Geodesic
Compact operators and integral equations in the $\cal {HK}$ space
Czechoslovak Mathematical Journal, Tome 72 (2022) no. 1, pp. 239-257

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.
DOI : 10.21136/CMJ.2021.0447-20
Classification : 26A39, 26A42
Keywords: compact operator; integral equation; controlled convergence; Henstock-Kurzweil integral 
@article{10_21136_CMJ_2021_0447_20,
     author = {Boonpogkrong, Varayu},
     title = {Compact operators and integral equations in the $\cal {HK}$ space},
     journal = {Czechoslovak Mathematical Journal},
     pages = {239--257},
     publisher = {mathdoc},
     volume = {72},
     number = {1},
     year = {2022},
     doi = {10.21136/CMJ.2021.0447-20},
     mrnumber = {4389117},
     zbl = {07511564},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2021.0447-20/}
}
TY  - JOUR
AU  - Boonpogkrong, Varayu
TI  - Compact operators and integral equations in the $\cal {HK}$ space
JO  - Czechoslovak Mathematical Journal
PY  - 2022
SP  - 239
EP  - 257
VL  - 72
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2021.0447-20/
DO  - 10.21136/CMJ.2021.0447-20
LA  - en
ID  - 10_21136_CMJ_2021_0447_20
ER  - 
%0 Journal Article
%A Boonpogkrong, Varayu
%T Compact operators and integral equations in the $\cal {HK}$ space
%J Czechoslovak Mathematical Journal
%D 2022
%P 239-257
%V 72
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2021.0447-20/
%R 10.21136/CMJ.2021.0447-20
%G en
%F 10_21136_CMJ_2021_0447_20
Boonpogkrong, Varayu. Compact operators and integral equations in the $\cal {HK}$ space. Czechoslovak Mathematical Journal, Tome 72 (2022) no. 1, pp. 239-257. doi: 10.21136/CMJ.2021.0447-20

Cité par Sources :