Local Bishop–Phelps–Bollobás properties

Sheldon Dantas; Sun Kwang Kim; Han Ju Lee; Martin Mazzitelli

doi:10.1016/j.jmaa.2018.08.015

Local Bishop–Phelps–Bollobás properties

Sheldon Dantas
, Sun Kwang Kim
, Han Ju Lee
, Martin Mazzitelli

Department of Mathematics Education

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

In this paper we introduce some local versions of Bishop–Phelps–Bollobás type property for operators. That is, the function η which appears in their definitions depends not only on a given ε>0, but also on either a fixed norm-one operator T or a fixed norm-one vector x. We investigate those properties and show differences between local and uniform versions.

Original language	English
Pages (from-to)	304-323
Number of pages	20
Journal	Journal of Mathematical Analysis and Applications
Volume	468
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2018.08.015
State	Published - 1 Dec 2018

Keywords

Banach space
Bishop–Phelps–Bollobás property
Norm attaining operators

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10.1016/j.jmaa.2018.08.015

Cite this

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title = "Local Bishop–Phelps–Bollob{\'a}s properties",

abstract = "In this paper we introduce some local versions of Bishop–Phelps–Bollob{\'a}s type property for operators. That is, the function η which appears in their definitions depends not only on a given ε>0, but also on either a fixed norm-one operator T or a fixed norm-one vector x. We investigate those properties and show differences between local and uniform versions.",

keywords = "Banach space, Bishop–Phelps–Bollob{\'a}s property, Norm attaining operators",

author = "Sheldon Dantas and Kim, \{Sun Kwang\} and Lee, \{Han Ju\} and Martin Mazzitelli",

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AU - Dantas, Sheldon

AU - Kim, Sun Kwang

AU - Lee, Han Ju

AU - Mazzitelli, Martin

PY - 2018/12/1

Y1 - 2018/12/1

N2 - In this paper we introduce some local versions of Bishop–Phelps–Bollobás type property for operators. That is, the function η which appears in their definitions depends not only on a given ε>0, but also on either a fixed norm-one operator T or a fixed norm-one vector x. We investigate those properties and show differences between local and uniform versions.

AB - In this paper we introduce some local versions of Bishop–Phelps–Bollobás type property for operators. That is, the function η which appears in their definitions depends not only on a given ε>0, but also on either a fixed norm-one operator T or a fixed norm-one vector x. We investigate those properties and show differences between local and uniform versions.

KW - Banach space

KW - Bishop–Phelps–Bollobás property

KW - Norm attaining operators

UR - https://www.scopus.com/pages/publications/85051782251

U2 - 10.1016/j.jmaa.2018.08.015

DO - 10.1016/j.jmaa.2018.08.015

M3 - Article

AN - SCOPUS:85051782251

SN - 0022-247X

VL - 468

SP - 304

EP - 323

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

Local Bishop–Phelps–Bollobás properties

Abstract

Keywords

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