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

Abstract.

This paper studies pure subnormal k-tuples of operators $\mathbb{S} = (S_{1} , \ldots ,S_{k} )$ with finite rank of self-commutators. It determines the substantial part of the conjugate of the joint point spectrum of $\mathbb{S}^{ * } = {\left( {S^{ * }_{1} , \ldots ,S^{ * }_{k} } \right)}$ which is the union of domains in Riemann surfaces in some algebraic varieties in $\mathbb{C}^{k} .$ The concrete form of the principal current [4] related to $\mathbb{S}$ is also determined. Besides, some operator identities are found for $\mathbb{S}.$