scholarly journals Geometric properties of noncommutative symmetric spaces of measurable operators and unitary matrix ideals

2017 ◽  
Vol 57 (1) ◽  
Author(s):  
Anna H. Kaminska ◽  
Malgorzata M. Czerwińska
Keyword(s):  
Symmetric Spaces ◽  
Unitary Matrix ◽  
Geometric Properties ◽  
Measurable Operators

Local uniform and uniform convexity of non-commutative symmetric spaces of measurable operators

1992 ◽  
Vol 111 (2) ◽  
pp. 355-368 ◽  
Author(s):  
Vladimir I. Chilin ◽  
Andrei V. Krygin ◽  
Pheodor A. Sukochev
Keyword(s):  
Banach Space ◽  
Sequence Space ◽  
Symmetric Spaces ◽  
Compact Operators ◽  
Uniform Convexity ◽  
Unitary Matrix ◽  
Matrix Space ◽  
Measurable Operators ◽  
Unitary Matrix Space ◽  
Matrix Spaces

Let E be a separable symmetric sequence space, and let CE be the unitary matrix space associated with E, i.e. the Banach space of all compact operators x on l2 so that s(x) E, with the norm , where are the s-numbers of x. One of the interesting subjects in the theory of the unitary matrix spaces is the clarification of correlation between the geometric properties of the spaces E and CE. A series of results in this direction related with the notions of type, cotype and uniform convexity of the spaces CE has been already obtained (see 13).

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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