On the Banach-Mazur Distance Between Continuous Function Spaces with Scattered Boundaries

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10475549" target="_blank" >RIV/00216208:11320/23:10475549 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=1rAtqESEQJ" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=1rAtqESEQJ</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.21136/CMJ.2023.0220-21" target="_blank" >10.21136/CMJ.2023.0220-21</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On the Banach-Mazur Distance Between Continuous Function Spaces with Scattered Boundaries

Popis výsledku v původním jazyce

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 spaces.

Název v anglickém jazyce

On the Banach-Mazur Distance Between Continuous Function Spaces with Scattered Boundaries

Popis výsledku anglicky

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 spaces.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Czechoslovak Mathematical Journal

ISSN

0011-4642

e-ISSN

1572-9141

Svazek periodika

73

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

CZ - Česká republika

Počet stran výsledku

27

Strana od-do

367-393

Kód UT WoS článku

000967229200001

EID výsledku v databázi Scopus

2-s2.0-85152404573