On the Pointwise Bishop-Phelps-Bollobas Property for Operators

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F19%3A00338240" target="_blank" >RIV/68407700:21230/19:00338240 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.4153/S0008414X18000032" target="_blank" >https://doi.org/10.4153/S0008414X18000032</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4153/S0008414X18000032" target="_blank" >10.4153/S0008414X18000032</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On the Pointwise Bishop-Phelps-Bollobas Property for Operators

Popis výsledku v původním jazyce

We study approximation of operators between Banach spaces X and Y that nearly attain their norms in a given point by operators that attain their norms at the same point. When such approximations exist, we say that the pair (X, Y) has the pointwise Bishop-Phelps-Bollobas property (pointwise BPB property for short). In this paper we mostly concentrate on those X, called universal pointwise BPB domain spaces, such that (X, Y) possesses pointwise BPB property for every Y, and on those Y, called universal pointwise BPB range spaces, such that (X, Y) enjoys pointwise BPB property for every uniformly smooth X. We show that every universal pointwise BPB domain space is uniformly convex and that L-p(mu) spaces fail to have this property when p > 2. No universal pointwise BPB range space can be simultaneously uniformly convex and uniformly smooth unless its dimension is one. We also discuss a version of the pointwise BPB property for compact operators.

Název v anglickém jazyce

On the Pointwise Bishop-Phelps-Bollobas Property for Operators

Popis výsledku anglicky

We study approximation of operators between Banach spaces X and Y that nearly attain their norms in a given point by operators that attain their norms at the same point. When such approximations exist, we say that the pair (X, Y) has the pointwise Bishop-Phelps-Bollobas property (pointwise BPB property for short). In this paper we mostly concentrate on those X, called universal pointwise BPB domain spaces, such that (X, Y) possesses pointwise BPB property for every Y, and on those Y, called universal pointwise BPB range spaces, such that (X, Y) enjoys pointwise BPB property for every uniformly smooth X. We show that every universal pointwise BPB domain space is uniformly convex and that L-p(mu) spaces fail to have this property when p > 2. No universal pointwise BPB range space can be simultaneously uniformly convex and uniformly smooth unless its dimension is one. We also discuss a version of the pointwise BPB property for compact operators.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/EF16_019%2F0000778" target="_blank" >EF16_019/0000778: Centrum pokročilých aplikovaných přírodních věd</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2019

Kód důvěrnosti údajů

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

Název periodika

Canadian Journal of Mathematics

ISSN

0008-414X

e-ISSN

1496-4279

Svazek periodika

71

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

23

Strana od-do

1421-1443

Kód UT WoS článku

000496552800006

EID výsledku v databázi Scopus

2-s2.0-85059301782