Approximate Birkhoff–James orthogonality and smoothness in the space of bounded linear operators

We study approximate Birkhoff–James orthogonality of bounded linear operators defined between normed linear spaces X and Y . As an application of the results obtained, we characterize smoothness of a bounded linear operator T under the condition that K ( X , Y ) , the space of compact linear operato...

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Bibliographic Details
Published inMonatshefte für Mathematik Vol. 190; no. 3; pp. 549 - 558
Main Authors Mal, Arpita, Paul, Kallol, Rao, T. S. S. R. K., Sain, Debmalya
Format Journal Article
LanguageEnglish
Published Vienna Springer Vienna 01.11.2019
Springer Nature B.V
Subjects
Linear operators
Mathematics
Mathematics and Statistics
Orthogonality
Smoothness
Vector spaces
Secondary 47L05
ideal
46B20
Orthogonality
Smoothness
Linear operators
Primary 46B28
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Summary:We study approximate Birkhoff–James orthogonality of bounded linear operators defined between normed linear spaces X and Y . As an application of the results obtained, we characterize smoothness of a bounded linear operator T under the condition that K ( X , Y ) , the space of compact linear operators is an M -ideal in L ( X , Y ) , the space of bounded linear operators.
ISSN:0026-9255
1436-5081
DOI:10.1007/s00605-019-01289-3