On the joint spectrum for n-tuples of hyponormal operators
Let \(A=(A_ 1,...,A_ n)\) be an n-tuple of doubly commuting hyponormal operators. It is proved that: 1. The joint spectrum of A has a Cartesian decomposition: \(Re[Sp(A)]=S_ p(Re A)\), \(Im[Sp(A)]=Sp(Im A);\) 2. The joint resolvent of A satisfies the growth condition: \(\| (A- s)^{\wedge}\| =1/dist(z,Sp(A));\) 3. If \(0\not\in \sigma (A_ i)\), \(i=1,2,...,n\), then \(\| A\| =r_{sp}(A)\).
scientific article; zbMATH DE number 3971557