Let and be C*-algebras such that or is exact.
We describe the largest ideal in
which has the
weak ideal property. For many C*-algebras and as above
we characterize when the largest ideal in
which
has the weak ideal property is the tensor product of the largest
ideals in and which have the weak ideal property (this is
not always true if or is exact). Assume that the C*-algebras
and have the weak ideal property (and one of them is
exact).
We characterize (in an interesting particular case and also in
general) when
has the weak ideal property (these
two characterizations are totally different in nature).

Key Words: Weak ideal property, tensor product C*-algebra, largest ideal which has the weak ideal property, primitive spectrum, ideal property.

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

Download the paper in pdf format here.