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There is no operatorwise version of the Bishop-Phelps-Bollobas property
- Issue Date
- 1-Sep-2020
- Publisher
- TAYLOR & FRANCIS LTD
- Keywords
- P; Semrl; Banach space; norm attaining operators; Bishop-Phelps-Bollobas property
- Citation
- LINEAR & MULTILINEAR ALGEBRA, v.68, no.9, pp 1767 - 1778
- Pages
- 12
- Indexed
- SCIE
SCOPUS
- Journal Title
- LINEAR & MULTILINEAR ALGEBRA
- Volume
- 68
- Number
- 9
- Start Page
- 1767
- End Page
- 1778
- ISSN
- 0308-1087
1563-5139
- Abstract
- Given two real Banach spacesXandYwith dimensions greater than one, it is shown that there is a sequence{Tn}n is an element of Nof norm attaining norm-one operators fromXtoYand a pointx0 is an element of Xwith parallel to x0 parallel to=1, such that parallel to Tn(x0)parallel to 1 but infn is an element of N{dist(x0,{x is an element of X:parallel to Tn(x)parallel to=parallel to x parallel to=1})}>0.This shows that a version of the Bishop-Phelps-Bollobas property in which the operator is not changed is possible only if one of the involved Banach spaces is one-dimensional.
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Related Researcher
- Lee, Han Ju
- College of Education (Department of Mathematics Education)