Complete functional calculus bounds for -contractions
arXiv:2607.13794
summary
The paper derives sharp, optimal bounds for the functional calculus of ρ‑contractions on Hilbert spaces when applied to matrix‑valued analytic functions on the unit disc, completing earlier partial results.
Abstract
Let be a -contraction on a Hilbert space. We establish sharp bounds for the functional calculus of for matrix-valued analytic functions on the unit disc. These are complete versions of bounds established by Drury and by Schwenninger and the second author.
15 pages
Topics & keywords
#operator theory#functional calculus#ρ-contractions#hilbert spaces#matrix-valued analytic functionsρ-contractionsharp boundsmatrix-valued analytic functionsunit discHilbert spacefunctional calculus