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.