functional analysis

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
Complete functional calculus bounds for $ρ$-contractions · wovepaper