Right Spectrum and Trace Formula of Subnormal Tuples of Operators of Finite Type

Abstract

This paper studies pure subnormal k-tuples of operators S = (S1, . . . , S k ) with finite rank of self-commutators. It determines the substantial part of the conjugate of the joint point spectrum of S * = (S * 1 , . . . , S * k ) which is the union of domains in Riemann surfaces in some algebraic varieties in C k . The concrete form of the principal current [4] related to S is also determined. Besides, some operator identities are found for S. (2000). Primary 47B20. Mathematics Subject Classification

A simple proof of Xia's proposition

“…be the right spectrum of T. In [1], D. Xia showed trace formula of subnormal tuples of operators of finite type. Also he showed the following proposition:…”