Norm attaining operators and renormings of Banach spaces

1983 ◽  
Vol 44 (3) ◽  
pp. 201-212 ◽  
Author(s):  
Walter Schachermayer
Keyword(s):  
Banach Spaces ◽  
Norm Attaining Operators ◽  
Norm Attaining

scholarly journals A NOTE ON L2-SUMMAND VECTORS IN DUAL SPACES

2008 ◽  
Vol 50 (3) ◽  
pp. 429-432 ◽  
Author(s):  
ANTONIO AIZPURU ◽  
FRANCISCO J GARCÍA-PACHECO
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Real Banach Space ◽  
Dual Spaces ◽  
Equivalent Norms ◽  
Norm Attaining

AbstractIt is shown that every L2-summand vector of a dual real Banach space is a norm-attaining functional. As consequences, the L2-summand vectors of a dual real Banach space can be determined by the L2-summand vectors of its predual; for every n ∈ , every real Banach space can be equivalently renormed so that the set of norm-attaining functionals is n-lineable; and it is easy to find equivalent norms on non-reflexive dual real Banach spaces that are not dual norms.

scholarly journals Norm Attaining Multilinear Forms on

2008 ◽  
Vol 2008 ◽  
pp. 1-6
Author(s):  
Yousef Saleh
Keyword(s):  
Banach Space ◽  
Linear Operators ◽  
Bilinear Forms ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Multilinear Forms ◽  
Arbitrary Measure ◽  
Norm Attaining Operators ◽  
Norm Attaining

Given an arbitrary measure , this study shows that the set of norm attaining multilinear forms is not dense in the space of all continuous multilinear forms on . However, we have the density if and only if is purely atomic. Furthermore, the study presents an example of a Banach space in which the set of norm attaining operators from into is dense in the space of all bounded linear operators . In contrast, the set of norm attaining bilinear forms on is not dense in the space of continuous bilinear forms on .

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