UPPER TRIANGULAR OPERATORS WITH SVEP Duggal, Bhagwati Prashad;
A Banach space operator A B(X) is polaroid if the isolated points of the spectrum of A are poles of the resolvent of A; A is hereditarily polaroid, A (), if every part of A is polaroid. Let , where are Banach spaces, and let A denote the class of upper triangular operators A = , and = 0 for i > j. We prove that operators A A such that for all , and have the single-valued extension property have spectral properties remarkably close to those of Jordan operators of order n and n-normal operators. Operators A A such that () for all are polaroid and have SVEP; hence they satisfy Weyl's theorem. Furthermore, A+R satisfies Browder's theorem for all upper triangular operators R, such that is a Riesz operator, which commutes with A.