Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5772413 | Journal of Functional Analysis | 2017 | 18 Pages |
Abstract
Let D denote the unit disc in the complex plane C and let D2=DÃD be the unit bidisc in C2. Let (T1,T2) be a pair of commuting contractions on a Hilbert space H. Let dimâ¡ran(IHâTjTjâ)<â, j=1,2, and let T1 be a pure contraction. Then there exists a variety VâDâ¾2 such that for any polynomial pâC[z1,z2], the inequalityâp(T1,T2)âB(H)â¤âpâV holds. If, in addition, T2 is pure, thenV={(z1,z2)âD2:detâ¡(Ψ(z1)âz2ICn)=0} is a distinguished variety, where Ψ is a matrix-valued analytic function on D that is unitary-valued on âD. Our results comprise a new proof, as well as a generalization, of Agler and McCarthy's sharper von Neumann inequality for pairs of commuting and strictly contractive matrices.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
B. Krishna Das, Jaydeb Sarkar,