**Memoirs of the American Mathematical Society**

2009;
91 pp;
Softcover

MSC: Primary 47;

Print ISBN: 978-0-8218-4396-3

Product Code: MEMO/200/941

List Price: $69.00

Individual Member Price: $41.40

**Electronic ISBN: 978-1-4704-0555-7
Product Code: MEMO/200/941.E**

List Price: $69.00

Individual Member Price: $41.40

# Unitary Invariants in Multivariable Operator Theory

Share this page
*Gelu Popescu*

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, Berger–Kato–Stampfli 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 Toeplitz-Hausdorff 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 \(F_n^\infty\).