scholarly journals A Note on the Operator Space Projective Tensor Product of C*-Algebras

2013 ◽  
Vol 03 (03) ◽  
pp. 176-180
Author(s):  
井先 季
Keyword(s):  
Tensor Product ◽  
Operator Space ◽  
Projective Tensor Product ◽  
C Algebras ◽  
Projective Tensor

scholarly journals IDEALS IN OPERATOR SPACE PROJECTIVE TENSOR PRODUCT OF C*-ALGEBRAS

2011 ◽  
Vol 91 (2) ◽  
pp. 275-288 ◽  
Author(s):  
RANJANA JAIN ◽  
AJAY KUMAR
Keyword(s):  
Tensor Product ◽  
Banach Algebra ◽  
Operator Space ◽  
Prime Ideals ◽  
Projective Tensor Product ◽  
C Algebras ◽  
Primitive Ideals ◽  
Projective Tensor

AbstractLet A and B be C*-algebras. We prove the slice map conjecture for ideals in the operator space projective tensor product $A \mathbin {\widehat {\otimes }} B$. As an application, a characterization of the prime ideals in the Banach *-algebra $A\mathbin {\widehat {\otimes }} B$ is obtained. In addition, we study the primitive ideals, modular ideals and the maximal modular ideals of $A\mathbin {\widehat {\otimes }} B$. We also show that the Banach *-algebra $A\mathbin {\widehat {\otimes }} B$ possesses the Wiener property and that, for a subhomogeneous C*-algebra A, the Banach * -algebra $A \mathbin {\widehat {\otimes }} B$ is symmetric.

scholarly journals The Operator Space Projective Tensor Product: Embedding into the Second Dual and Ideal Structure

2013 ◽  
Vol 57 (2) ◽  
pp. 505-519 ◽  
Author(s):  
Ranjana Jain ◽  
Ajay Kumar
Keyword(s):  
Tensor Product ◽  
Bilinear Form ◽  
Operator Space ◽  
Ideal Structure ◽  
Operator Spaces ◽  
Canonical Embedding ◽  
Projective Tensor Product ◽  
Projective Tensor ◽  
Second Dual ◽  
Continuous Inverse

AbstractWe prove that, for operator spaces V and W, the operator space V** ⊗hW** can be completely isometrically embedded into (V ⊗hW)**, ⊗h being the Haagerup tensor product. We also show that, for exact operator spaces V and W, a jointly completely bounded bilinear form on V × W can be extended uniquely to a separately w*-continuous jointly completely bounded bilinear form on V× W**. This paves the way to obtaining a canonical embedding of into with a continuous inverse, where is the operator space projective tensor product. Further, for C*-algebras A and B, we study the (closed) ideal structure of which, in particular, determines the lattice of closed ideals of completely.

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.

A New Approach to Operator Spaces

1991 ◽  
Vol 34 (3) ◽  
pp. 329-337 ◽  
Author(s):  
Edward G. Effros ◽  
Zhong-Jin Ruan
Keyword(s):  
Banach Space ◽  
Tensor Product ◽  
Banach Spaces ◽  
Operator Space ◽  
Operator Spaces ◽  
New Approach ◽  
Projective Tensor Product ◽  
Projective Tensor ◽  
Space Concepts ◽  
Injective Operator

AbstractThe authors previously observed that the space of completely bounded maps between two operator spaces can be realized as an operator space. In particular, with the appropriate matricial norms the dual of an operator space V is completely isometric to a linear space of operators. This approach to duality enables one to formulate new analogues of Banach space concepts and results. In particular, there is an operator space version ⊗μ of the Banach space projective tensor product , which satisfies the expected functorial properties. As is the case for Banach spaces, given an operator space V, the functor W |—> V ⊗μ W preserves inclusions if and only if is an injective operator space.

scholarly journals The dual of the space of bounded operators on a Banach space

2021 ◽  
Vol 8 (1) ◽  
pp. 48-59
Author(s):  
Fernanda Botelho ◽  
Richard J. Fleming
Keyword(s):  
Banach Space ◽  
Tensor Product ◽  
Banach Spaces ◽  
Dual Space ◽  
Tensor Products ◽  
Bounded Operators ◽  
Projective Tensor Product ◽  
Projective Tensor

Abstract Given Banach spaces X and Y, we ask about the dual space of the 𝒧(X, Y). This paper surveys results on tensor products of Banach spaces with the main objective of describing the dual of spaces of bounded operators. In several cases and under a variety of assumptions on X and Y, the answer can best be given as the projective tensor product of X ** and Y *.

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