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On the Bishop-Phelps-Bollobas theorem for operators and numerical radius
- Authors
- Kim, Sun Kwang; Lee, Han Ju; Martin, Miguel
- Issue Date
- 2016
- Publisher
- POLISH ACAD SCIENCES INST MATHEMATICS-IMPAN
- Keywords
- Banach space; approximation; numerical radius attaining operators; Bishop Phelps Bollobas theorem
- Citation
- STUDIA MATHEMATICA, v.233, no.2, pp 141 - 151
- Pages
- 11
- Indexed
- SCI
SCIE
SCOPUS
- Journal Title
- STUDIA MATHEMATICA
- Volume
- 233
- Number
- 2
- Start Page
- 141
- End Page
- 151
- ISSN
- 0039-3223
1730-6337
- Abstract
- We study the Bishop-Phelps-Bollobas property for numerical radius (for short, BPBp-nu) of operators on l(1)-sums and l(infinity)-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 circle plus(1) Y has the weak BPBp-nu, then (X, Y) has the Bishop-Phelps-Bollobas property (BPBp). On the other hand, if Y is strongly lush and X circle plus(infinity) Y has the weak BPBp-nu, then (X, Y) has the BPBp. Examples of strongly lush spaces are C(K) spaces, L-1(mu) spaces, and finite-codimensional subspaces of C[0, 1].
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Related Researcher
- Lee, Han Ju
- College of Education (Department of Mathematics Education)