Smooth points in spaces of operators

For Banach spaces X, Y, in the space of bounded linear operators L(X,Y), we examine the relation between T∈L(X,Y) being a smooth point versus T⁎∈L(Y⁎,X⁎) being a smooth point. Motivated by some results in the recent paper of Paul et al., we give some sufficient conditions for the validity of such a...

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Bibliographic Details
Published inLinear algebra and its applications Vol. 517; pp. 129 - 133
Main Author Rao, T.S.S.R.K.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier Inc 15.03.2017
American Elsevier Company, Inc
Subjects
Banach spaces
Hahn–Banach smooth spaces
Linear algebra
Linear operators
Mathematical functions
Smooth points
Spaces of operators
Spaces of operators
Smooth points
Hahn–Banach smooth spaces
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Summary:For Banach spaces X, Y, in the space of bounded linear operators L(X,Y), we examine the relation between T∈L(X,Y) being a smooth point versus T⁎∈L(Y⁎,X⁎) being a smooth point. Motivated by some results in the recent paper of Paul et al., we give some sufficient conditions for the validity of such a statement for spaces of operators.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2016.12.011