PASSAGE OF PROPERTY (gw) FROM TWO OPERATORS TO THEIR TENSOR PRODUCT

Abstract

A Banach space operator satisfies property (gw) if the complement of its B-Weyl essential approximate point spectrum in its approximate point spectrum is the set of isolated eigenvalues of the operator.  We give necessary and/or sufficient conditions ensuring the passage of property (gw) from two Banach space operators A and B to their tensor product.  In particular, we present a revised version of Theorem 2.3 in [20].