  In this paper, one of our main purposes is to prove the boundedness of
solution set of tensor complementarity problem with B tensor such that the
specific bounds only depend on the structural properties of tensor. To achieve
this purpose, firstly, we present that each B tensor is strictly semi-positive
and each B$_0$ tensor is semi-positive. Subsequencely, the strictly lower and
upper bounds of different operator norms are given for two positively
homogeneous operators defined by B tensor. Finally, with the help of the upper
bounds of different operator norms, we show the strcitly lower bound of
solution set of tensor complementarity problem with B tensor. Furthermore, the
upper bounds of spectral radius and $E$-spectral radius of B (B$_0$) tensor are
obtained, respectively, which achieves our another objective. In particular,
such the upper bounds only depend on the principal diagonal entries of tensors.
