Limit Points for Browder Spectrum of Operator Matrices

Let $A\in \mathcal{B}(X)$ and $B\in \mathcal{B}(Y)$, where $X$ and $Y$ are Banach spaces, and let $M_C$ be an operator acting on $X\oplus Y$ given by $M_C=\left(\begin{array}{cc}A& C\\ 0& B\end{array}\right)$. We investigate the limit point set of the Browder spectrum of $M_C$. It is shown that $$acc{\sigma }_b(M_C)\cup W_{acc{\sigma }_b}=acc{\sigma }_b(A)\cup acc{\sigma }_b(B)$$ where $W_{acc{\sigma }_b}$ is a subsets of $acc{\sigma }_{\ast }(B)\cap acc{\sigma }_{\ast }(A)$ and a union of certain holes in $ acc \sigma_{b}(M_C)$\mathrm{.}Furthermore,severalsufficientconditionsfor$acc\sigma_{b}(M_C)=acc\sigma_{b}(A)\cup acc\sigma_{b}(B)$holdsforevery$C\in $\mathcal{B}$(Y,X)$ are given.