Browder-Weyl theorems, tensor products and multiplications

A Banach space operator T is an element of B(X) satisfies Browder's theorem if the complement of the Weyl spectrum sigma(w)(T) of T in sigma(T) equals the set of Riesz points of T; T is polaroid if the isolated points of sigma(T) are poles (no restriction on rank) of the resolvent of T. Let Phi(T) denote the set of Fredholm points of T. Browder's theorem transfers from A, B is an element of B(X) to S = LARB (resp., S = A circle times B) if and only if A and B* (resp., A and B) have SVEP at points mu is an element of Phi(A) and nu is an element of Phi(B) for which lambda = mu nu is not an element of sigma(w) (S). If A and B are finitely polaraid, then the polaroid property transfers from A is an element of B(X) and B is an element of B(Y) to LARB; again, restricting ourselves to the completion of X circle times Y in the projective topology, if A and B are finitely polaroid, then the polaroid property transfers from A is an element of B(X) and B is an element of B(Y) to A circle times B. (C) 2009 Elsevier Inc. All rights reserved.