We prove an
 $n$-tuple analogue of the Putnam area inequality for the spectrum of a
 single $p$-hyponormal operator.

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A Putnam area inequality for the spectrum of n -tuples of p -hyponormal operators

Taylor and Xia spectra of p-hyponormal n-tuples

In the past ten years the theory of operators on Hilbert space made great progress. The fundamental problems are: (1) To determine the spectrum of an operator and discuss the properties of its resolvent. (2) To determine the relations of the spectra between operators. (3) To determine the structure of an operator or to give a concrete model of a class of operators. These problems are difficult and complex. We discuss these problems in some special classes of operators.

Advance of Operator Theory in Fudan University

The main purpose of the present paper is to describe the Taylor joint spectra forn-tuples of double commuting hyponormal operators, and to study the representation of the joint spectra in terms of that ofn-tuples of commuting normal operators.

Huang Chaocheng

Papers

On the representation of the joint spectrum for a commutingn-tuple of non-normal operators