In this paper, we find necessary and sufficient conditions for Banach Space operator to satisfy the property (Bb). Then we obtain, if Banach Space operators $A\in B(X)$ and $B\in B(Y)$ satisfy property (Bb) implies $A\otimes B$ satisfy property (Bb) if and only if the B-Weyl spectrum identity $\sigma_{BW}(A\otimes B)=\sigma_{BW}(A)\sigma(B)\cup\sigma_{BW}(B)\sigma(A)$ holds. Perturbations by Riesz operators are considered.