Complete functional calculus bounds for $ρ$-contractions

Michael Hartz; Jens de Vries

Complete functional calculus bounds for $ρ$-contractions

Functional Analysis 2026-07-15 v1

Authors: Michael Hartz , Jens de Vries

Abstract

Let $T$ be a $\rho$ -contraction on a Hilbert space. We establish sharp bounds for the functional calculus of $T$ 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.

Cite

@article{arxiv.2607.13794,
  title  = {Complete functional calculus bounds for $ρ$-contractions},
  author = {Michael Hartz and Jens de Vries},
  journal= {arXiv preprint arXiv:2607.13794},
  year   = {2026}
}

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15 pages