Some remarks on minimum norm attaining operators

2020 ◽  
Vol 492 (2) ◽  
pp. 124492
Author(s):  
Uday Shankar Chakraborty
Keyword(s):  
Minimum Norm ◽  
Norm Attaining Operators ◽  
Norm Attaining

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 .

scholarly journals Another unitarily invariant norm attaining the minimum norm bound for commutators

2010 ◽  
Vol 433 (11-12) ◽  
pp. 1793-1797 ◽  
Author(s):  
Kin-Sio Fong ◽  
Che-Man Cheng ◽  
Io-Kei Lok
Keyword(s):  
Unitarily Invariant Norm ◽  
Minimum Norm ◽  
Invariant Norm ◽  
Norm Bound ◽  
Norm Attaining

Norm-attaining operators into Lorentz sequence spaces

2009 ◽  
Vol 139 (2) ◽  
pp. 225-235 ◽  
Author(s):  
María D. Acosta
Keyword(s):  
Orlicz Space ◽  
Sequence Space ◽  
Orlicz Function ◽  
Linear Operators ◽  
Sequence Spaces ◽  
Norm Attaining Operators ◽  
Norm Attaining ◽  
Admissible Sequences

We prove that the Lorentz sequence spaces do not have the property B of Lindenstrauss. In fact, for any admissible sequences w, v ∈ c0 \ l1, the set of norm-attaining operators from the Orlicz space hϕ(w) (ϕ is a certain Orlicz function) into d(v, 1) is not dense in the corresponding space of operators. We also characterize the spaces such that the subset of norm-attaining operators from the Marcinkiewicz sequence space into its dual is dense in the space of all bounded and linear operators between them.

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