2 results
Schur Multipliers of Cartan Pairs
- Part of
-
- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 60 / Issue 2 / May 2017
- Published online by Cambridge University Press:
- 13 June 2016, pp. 413-440
-
- Article
- Export citation
-
We define the Schur multipliers of a separable von Neumann algebra
with Cartan maximal abelian self-adjoint algebra 
, generalizing the classical Schur multipliers of 
(ℓ2). We characterize these as the normal -bimodule maps on . If contains a direct summand isomorphic to the hyperfinite II1 factor, then we show that the Schur multipliers arising from the extended Haagerup tensor product ⊗eh are strictly contained in the algebra of all Schur multipliers.
with Cartan maximal abelian self-adjoint algebra 
, generalizing the classical Schur multipliers of 
(BIPROJECTIVITY AND BIFLATNESS OF LAU PRODUCT OF BANACH ALGEBRAS DEFINED BY A BANACH ALGEBRA MORPHISM
- Part of
-
- Journal:
- Bulletin of the Australian Mathematical Society / Volume 91 / Issue 1 / February 2015
- Published online by Cambridge University Press:
- 15 July 2014, pp. 134-144
- Print publication:
- February 2015
-
- Article
-
- You have access
- Export citation
-
Let
${\it\varphi}$ be a homomorphism from a Banach algebra 
${\mathcal{B}}$ to a Banach algebra 
${\mathcal{A}}$. We define a multiplication on the Cartesian product space 
${\mathcal{A}}\times {\mathcal{B}}$ and obtain a new Banach algebra 
${\mathcal{A}}\times _{{\it\varphi}}{\mathcal{B}}$. We show that biprojectivity as well as biflatness of 
${\mathcal{A}}\times _{{\it\varphi}}{\mathcal{B}}$ are stable with respect to 
${\it\varphi}$.
