Memoirs of the American Mathematical Society 2009; 91 pp; softcover Volume: 200 ISBN10: 0821843966 ISBN13: 9780821843963 List Price: US$69 Individual Members: US$41.40 Institutional Members: US$55.20 Order Code: MEMO/200/941
 This paper concerns unitary invariants for \(n\)tuples \(T:=(T_1,\ldots, T_n)\) of (not necessarily commuting) bounded linear operators on Hilbert spaces. The author introduces a notion of joint numerical radius and works out its basic properties. Multivariable versions of Berger's dilation theorem, BergerKatoStampfli mapping theorem, and Schwarz's lemma from complex analysis are obtained. The author studies the joint (spatial) numerical range of \(T\) in connection with several unitary invariants for \(n\)tuples of operators such as: right joint spectrum, joint numerical radius, euclidean operator radius, and joint spectral radius. He also proves an analogue of ToeplitzHausdorff theorem on the convexity of the spatial numerical range of an operator on a Hilbert space, for the joint numerical range of operators in the noncommutative analytic Toeplitz algebra \(F_n^\infty\). Table of Contents  Introduction
 Unitary invariants for \(n\)tuples of operators
 Joint operator radii, inequalities, and applications
 Bibliography
