The Bishop-Phelps-Bollobás theorem for operators from ℓ1 sums of Banach spaces

Sun Kwang Kim; Han Ju Lee; Miguel Martín

doi:10.1016/j.jmaa.2015.03.057

The Bishop-Phelps-Bollobás theorem for operators from ℓ₁ sums of Banach spaces

Sun Kwang Kim, Han Ju Lee, Miguel Martín

Department of Mathematics Education

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

6 Scopus citations

Abstract

We introduce a generalized approximate hyperplane series property for a pair (X, Y) of Banach spaces to characterize when (ℓ₁(X), Y) has the Bishop-Phelps-Bollobás property. In particular, we show that (X, Y) has this property if X, Y are finite-dimensional, if X is a C(K) space and Y is a Hilbert space, or if X is Asplund and Y=C₀(L), where K is a compact Hausdorff space and L is a locally compact Hausdorff space.

Original language	English
Pages (from-to)	920-929
Number of pages	10
Journal	Journal of Mathematical Analysis and Applications
Volume	428
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2015.03.057
State	Published - 15 Aug 2015

Keywords

Bishop-Phelps theorem
Norm attaining operators

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title = "The Bishop-Phelps-Bollob{\'a}s theorem for operators from ℓ1 sums of Banach spaces",

abstract = "We introduce a generalized approximate hyperplane series property for a pair (X, Y) of Banach spaces to characterize when (ℓ1(X), Y) has the Bishop-Phelps-Bollob{\'a}s property. In particular, we show that (X, Y) has this property if X, Y are finite-dimensional, if X is a C(K) space and Y is a Hilbert space, or if X is Asplund and Y=C0(L), where K is a compact Hausdorff space and L is a locally compact Hausdorff space.",

keywords = "Bishop-Phelps theorem, Norm attaining operators",

author = "Kim, {Sun Kwang} and Lee, {Han Ju} and Miguel Mart{\'i}n",

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AU - Lee, Han Ju

AU - Martín, Miguel

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Y1 - 2015/8/15

N2 - We introduce a generalized approximate hyperplane series property for a pair (X, Y) of Banach spaces to characterize when (ℓ1(X), Y) has the Bishop-Phelps-Bollobás property. In particular, we show that (X, Y) has this property if X, Y are finite-dimensional, if X is a C(K) space and Y is a Hilbert space, or if X is Asplund and Y=C0(L), where K is a compact Hausdorff space and L is a locally compact Hausdorff space.

AB - We introduce a generalized approximate hyperplane series property for a pair (X, Y) of Banach spaces to characterize when (ℓ1(X), Y) has the Bishop-Phelps-Bollobás property. In particular, we show that (X, Y) has this property if X, Y are finite-dimensional, if X is a C(K) space and Y is a Hilbert space, or if X is Asplund and Y=C0(L), where K is a compact Hausdorff space and L is a locally compact Hausdorff space.

KW - Bishop-Phelps theorem

KW - Norm attaining operators

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JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

The Bishop-Phelps-Bollobás theorem for operators from ℓ₁ sums of Banach spaces

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Keywords

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