scholarly journals Complex uniform rotundity in symmetric spaces of measurable operators

2012 ◽  
Vol 395 (2) ◽  
pp. 501-508
Author(s):  
M.M. Czerwińska
Keyword(s):  
Symmetric Spaces ◽  
Uniform Rotundity ◽  
Measurable Operators

scholarly journals Erratum to: Banach envelopes in symmetric spaces of measurable operators

Positivity ◽  
2016 ◽  
Vol 21 (1) ◽  
pp. 493-493
Author(s):  
M. M. Czerwińska ◽  
A. Kamińska
Keyword(s):  
Symmetric Spaces ◽  
Measurable Operators

scholarly journals Banach envelopes in symmetric spaces of measurable operators

Positivity ◽  
2016 ◽  
Vol 21 (1) ◽  
pp. 473-492
Author(s):  
M. M. Czerwińska ◽  
A. Kamińska
Keyword(s):  
Symmetric Spaces ◽  
Measurable Operators

scholarly journals Local Uniform Convexity and Kadec-Klee Type Properties inK-interpolation spaces II

2004 ◽  
Vol 2 (3) ◽  
pp. 323-356 ◽  
Author(s):  
Peter G. Dodds ◽  
Theresa K. Dodds ◽  
Alexander A. Sedaev ◽  
Fyodor A. Sukochev
Keyword(s):  
Parameter Space ◽  
Wide Class ◽  
Symmetric Spaces ◽  
Interpolation Method ◽  
Function Spaces ◽  
Uniform Convexity ◽  
Interpolation Spaces ◽  
Banach Function Spaces ◽  
Measurable Operators ◽  
Order Continuous

We study local uniform convexity and Kadec-Klee type properties inK-interpolation spaces of Lorentz couples. We show that a wide class of Banach couples of (commutative and) non-commutative Lorentz spaces possess the (so-alled) (DGL)-property originally introduced by Davis, Ghoussoub and Lindenstrauss in the context of renorming order continuous Banach latties. This property is used as a key tool to show that local uniform convexity and certain Kadec-Klee type properties in non-commutative symmetric spaces of measurable operators may be inferred from corresponding properties of the parameter space of theK-interpolation method. Further applications are given to renorming properties of separable symmetric Banach function spaces and their non-commutative counterparts.

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