By Gelu Popescu
This paper issues unitary invariants for n-tuples T:=(Tl,...,Tn) of (not inevitably commuting) bounded linear operators on Hilbert areas. the writer introduces a proposal of joint numerical radius and works out its easy homes. Multivariable types of Berger's dilation theorem, Berger - Kato - Stampfli mapping theorem, and Schwarz's lemma from advanced research are bought. the writer reports the joint (spatial) numerical variety of T in reference to a number of unitary invariants for n-tuples of operators equivalent to: correct joint spectrum, joint numerical radius, euclidean operator radius, and joint spectral radius. He additionally proves an analogue of Toeplitz-Hausdorff theorem at the convexity of the spatial numerical variety of an operator on a Hilbert area, for the joint numerical variety of operators within the noncommutative analytic Toeplitz algebra Fn.
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