Cornel Pasnicu: On and around the weak ideal property, 199-204

Abstract:

If $A$ and $B$ are C*-algebras that have the weak ideal property and one of them is exact, does the minimal tensor product $A \otimes B$ have the weak ideal property? This question, and the similar one for residual (SP), have been asked in [7]. In this short note we give some results related to these questions, considering slight modifications of the definitions of the weak ideal property and of residual (SP).

Key Words: Weak ideal property, property (SP), residual (SP), topological dimension zero, the ideal property.

2010 Mathematics Subject Classification: Primary 46L06; Secondary 46L05.