be C*-algebras such that
We describe the largest ideal in
which has the
weak ideal property. For many C*-algebras
we characterize when the largest ideal in
has the weak ideal property is the tensor product of the largest
which have the weak ideal property (this is
not always true if
is exact). Assume that the C*-algebras
have the weak ideal property (and one of them is
We characterize (in an interesting particular case and also in
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.
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