The Bishop-Phelps-Bollobas Property and Absolute Sums
SCIE
SCOPUS
- Title
- The Bishop-Phelps-Bollobas Property and Absolute Sums
- Authors
- Choi, Yun Sung; Dantas, Sheldon; Jung, Mingu; Martin, Miguel
- Date Issued
- 2019-06
- Publisher
- SPRINGER BASEL AG
- Abstract
- In this paper, we study conditions assuring that the Bishop-Phelps-Bollobas property (BPBp, for short) is inherited by absolute summands of the range space or of the domain space. Concretely, given a pair (X,Y) of Banach spaces having the BPBp, if Y1 is an absolute summand of Y, then (X,Y1) has the BPBp;if X1 is an absolute summand of X of type 1 or , then (X1,Y) has the BPBp. Besides, analogous results for the BPBp for compact operators and for the density of norm-attaining operators are also given. We also show that the Bishop-Phelps-Bollobas property for numerical radius is inherited by absolute summands of type 1 or . Moreover, we provide analogous results for numerical radius attaining operators and for the BPBp for numerical radius for compact operators.
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/100835
- DOI
- 10.1007/s00009-019-1346-6
- ISSN
- 1660-5446
- Article Type
- Article
- Citation
- MEDITERRANEAN JOURNAL OF MATHEMATICS, vol. 16, no. 3, 2019-06
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