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Right Spectrum and Trace Formula of Subnormal Tuples of Operators of Finite Type
Authors:Daoxing Xia
Affiliation:(1) Department of Mathematics, Vanderbilt University, Nashville, TN 37240, USA
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 $$mathbb{S}.$$
Keywords:Primary 47B20
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