Geodesic
On the Banach-Mazur distance between continuous function spaces with scattered boundaries
Czechoslovak Mathematical Journal, Tome 73 (2023) no. 2, pp. 367-393.

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

We study the dependence of the Banach-Mazur distance between two subspaces of vector-valued continuous functions on the scattered structure of their boundaries. In the spirit of a result of Y. Gordon (1970), we show that the constant $2$ appearing in the Amir-Cambern theorem may be replaced by $3$ for some class of subspaces. We achieve this by showing that the Banach-Mazur distance of two function spaces is at least 3, if the height of the set of weak peak points of one of the spaces differs from the height of a closed boundary of the second space. Next we show that this estimate can be improved if the considered heights are finite and significantly different. As a corollary, we obtain new results even for the case of $\mathcal C(K, E)$ spaces.
DOI : 10.21136/CMJ.2023.0220-21
Classification : 46A55, 46B03, 46E40
Keywords: function space; vector-valued Amir-Cambern theorem; scattered space; Banach-Mazur distance; closed boundary 
@article{10_21136_CMJ_2023_0220_21,
     author = {Rondo\v{s}, Jakub},
     title = {On the {Banach-Mazur} distance between continuous function spaces with scattered boundaries},
     journal = {Czechoslovak Mathematical Journal},
     pages = {367--393},
     publisher = {mathdoc},
     volume = {73},
     number = {2},
     year = {2023},
     doi = {10.21136/CMJ.2023.0220-21},
     mrnumber = {4586900},
     zbl = {07729513},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2023.0220-21/}
}
TY  - JOUR
AU  - Rondoš, Jakub
TI  - On the Banach-Mazur distance between continuous function spaces with scattered boundaries
JO  - Czechoslovak Mathematical Journal
PY  - 2023
SP  - 367
EP  - 393
VL  - 73
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2023.0220-21/
DO  - 10.21136/CMJ.2023.0220-21
LA  - en
ID  - 10_21136_CMJ_2023_0220_21
ER  - 
%0 Journal Article
%A Rondoš, Jakub
%T On the Banach-Mazur distance between continuous function spaces with scattered boundaries
%J Czechoslovak Mathematical Journal
%D 2023
%P 367-393
%V 73
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2023.0220-21/
%R 10.21136/CMJ.2023.0220-21
%G en
%F 10_21136_CMJ_2023_0220_21
Rondoš, Jakub. On the Banach-Mazur distance between continuous function spaces with scattered boundaries. Czechoslovak Mathematical Journal, Tome 73 (2023) no. 2, pp. 367-393. doi : 10.21136/CMJ.2023.0220-21. http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2023.0220-21/

Cité par Sources :