On the Bishop-Phelps-Bollobás theorem for operators and numerical radius

Sun Kwang Kim, Han Ju Lee, and Miguel Martín. "On the Bishop-Phelps-Bollobás theorem for operators and numerical radius." Studia Mathematica 233.2 (2016): 141-151. <http://eudml.org/doc/285608>.

@article{SunKwangKim2016,
abstract = {We study the Bishop-Phelps-Bollobás property for numerical radius (for short, BPBp-nu) of operators on ℓ₁-sums and $ℓ_\{∞\}$-sums of Banach spaces. More precisely, we introduce a property of Banach spaces, which we call strongly lush. We find that if X is strongly lush and X ⊕₁ Y has the weak BPBp-nu, then (X,Y) has the Bishop-Phelps-Bollobás property (BPBp). On the other hand, if Y is strongly lush and $X ⊕_\{∞\} Y$ has the weak BPBp-nu, then (X,Y) has the BPBp. Examples of strongly lush spaces are C(K) spaces, L₁(μ) spaces, and finite-codimensional subspaces of C[0,1].},
author = {Sun Kwang Kim, Han Ju Lee, Miguel Martín},
journal = {Studia Mathematica},
keywords = {Banach space; approximation; numerical radius attaining operators; Bishop-Phelps-Bollob'as theorem},
language = {eng},
number = {2},
pages = {141-151},
title = {On the Bishop-Phelps-Bollobás theorem for operators and numerical radius},
url = {http://eudml.org/doc/285608},
volume = {233},
year = {2016},
}

TY - JOUR
AU - Sun Kwang Kim
AU - Han Ju Lee
AU - Miguel Martín
TI - On the Bishop-Phelps-Bollobás theorem for operators and numerical radius
JO - Studia Mathematica
PY - 2016
VL - 233
IS - 2
SP - 141
EP - 151
AB - We study the Bishop-Phelps-Bollobás property for numerical radius (for short, BPBp-nu) of operators on ℓ₁-sums and $ℓ_{∞}$-sums of Banach spaces. More precisely, we introduce a property of Banach spaces, which we call strongly lush. We find that if X is strongly lush and X ⊕₁ Y has the weak BPBp-nu, then (X,Y) has the Bishop-Phelps-Bollobás property (BPBp). On the other hand, if Y is strongly lush and $X ⊕_{∞} Y$ has the weak BPBp-nu, then (X,Y) has the BPBp. Examples of strongly lush spaces are C(K) spaces, L₁(μ) spaces, and finite-codimensional subspaces of C[0,1].
LA - eng
KW - Banach space; approximation; numerical radius attaining operators; Bishop-Phelps-Bollob'as theorem
UR - http://eudml.org/doc/285608
ER -