Browder spectra and essential spectra of operator matrices

Let be a 2 × 2 upper triangular operator matrix acting on the Banach space X × Y. We prove that where W is the union of certain of the holes in σ _τ (M _C ) which happen to be subsets of σ _τ (A) ∩ σ _τ (B), and σ _τ (A), σ _τ (B), σ _τ (M _C ) can be equal to the Browder or essential spectra of A, B, M _C , respectively. We also show that the above result isn’t true for the Kato spectrum, left (right) essential spectrum and left (right) spectrum. This work was supported by the National Natural Science Foundation of China (Grants NO.10471025, NO.10771034), the Natural Science Foundation of Fujian Province of China(Grant NO.S0650009), the Education Department Foundation of Fujian Province of China (Grants NO.JA05211, NO.JB06026) and the Foundation of Technology and Development of Fuzhou University(Grant NO.2007-XY-11)