scholarly journals A Note on Submaximal Operator Space Structures

2015 ◽  
pp. 185-194
Author(s):  
P. Vinod Kumar ◽  
M. S. Balasubramani
Keyword(s):  
Operator Space ◽  
Space Structures

scholarly journals Submaximal operator space structures on Banach spaces

2013 ◽  
pp. 723-732
Author(s):  
Chunyan Deng ◽  
M. S. Balasubramani
Keyword(s):  
Banach Spaces ◽  
Operator Space ◽  
Space Structures

scholarly journals Rigid $\mathcal{OL}_p$structures of non-commutative $L_p$-spaces associated with hyperfinite von Neumann algebras

2005 ◽  
Vol 96 (1) ◽  
pp. 63 ◽  
Author(s):  
Marius Junge ◽  
Zhong-Jin Ruan ◽  
Quanhua Xu
Keyword(s):  
Von Neumann Algebra ◽  
Von Neumann Algebras ◽  
Operator Space ◽  
Local Operator ◽  
Space Structures ◽  
Von Neumann ◽  
Local Properties

This paper is devoted to the study of rigid local operator space structures on non-commutative $L_p$-spaces. We show that for $1\le p \neq 2 < \infty$, a non-commutative $L_p$-space $L_p(\mathcal M)$ is a rigid $\mathcal{OL}_p$ space (equivalently, a rigid $\mathcal{COL}_p$ space) if and only if it is a matrix orderly rigid $\mathcal{OL}_p$ space (equivalently, a matrix orderly rigid $\mathcal{COL}_p$ space). We also show that $L_p(\mathcal M)$ has these local properties if and only if the associated von Neumann algebra $\mathcal M$ is hyperfinite. Therefore, these local operator space properties on non-commutative $L_p$-spaces characterize hyperfinite von Neumann algebras.

scholarly journals On Minimal and Maximal p-operator Space Structures

2014 ◽  
Vol 57 (1) ◽  
pp. 166-177
Author(s):  
Serap Öztop ◽  
Nico Spronk
Keyword(s):  
Tensor Product ◽  
Space Structure ◽  
Operator Space ◽  
Multiplication Operators ◽  
Space Structures ◽  
Projective Tensor Product ◽  
Projective Tensor ◽  
Operator Space Structure ◽  
Decomposable Measure

AbstractWe show that L∞(µ), in its capacity as multiplication operators on Lp(µ), is minimal as a p-operator space for a decomposable measure μ. We conclude that L1(μ) has a certain maximal type p-operator space structure that facilitates computations with L1(μ) and the projective tensor product.

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