Advances in Operator Theory

Multicentric holomorphic calculus for $n-$tuples of commuting operators

ِDiana Andrei

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

‎‎In multicentric holomorphic calculus‎, ‎one represents the function $\varphi$‎, ‎using a new polynomial variable $w=p(z),$ $z\in \mathbb{C},$ in such a way that when it is evaluated at the operator $T,$ then $p(T)$ is small in norm‎. ‎Usually it is assumed that $p$ has distinct roots‎. ‎In this paper we aim to extend this multicentric holomorphic calculus to $n$-tuples of commuting operators looking in particular at the case when $n=2$‎.

Article information

Source
Adv. Oper. Theory, Volume 4, Number 2 (2019), 447-461.

Dates
Received: 16 April 2018
Accepted: 2 October 2018
First available in Project Euclid: 1 December 2018

Permanent link to this document
https://projecteuclid.org/euclid.aot/1543633237

Digital Object Identifier
doi:10.15352/aot.1804-1346

Mathematical Reviews number (MathSciNet)
MR3883146

Subjects
Primary: 47A60: Functional calculus
Secondary: 46E20‎ ‎47A13‎ ‎47A25

Keywords
multicentric calculus‎‎ ‎commuting operator ‎ ‎lemniscate‎ ‎ ‎von Neumann's inequality‎ ‎ ‎homogeneous polynomial

Citation

Andrei, ِDiana. Multicentric holomorphic calculus for $n-$tuples of commuting operators. Adv. Oper. Theory 4 (2019), no. 2, 447--461. doi:10.15352/aot.1804-1346. https://projecteuclid.org/euclid.aot/1543633237


Export citation

References

  • T. Andô, On a pair of commuting contractions, Acta Sci. Math. (Szeged) 24 (1963), 88–90.
  • D. Apetrei and O. Nevanlinna, Multicentric calculus and the Riesz projection, J. Numer. Anal. Approx. Theory 44 (2016), no. 2, 127–145.
  • C. Benhida and E.H. Zerouali On Taylor and other joint spectra for commuting n-tuples of operators, J. Math. Anal. Appl. 326 (2007), no. 1, 521–532.
  • P. G. Dixon, The von Neumann inequality for polynomials of degree grater than two, J. London Math. Soc. (2) 14 (1976), no. 2, 369–375.
  • D. Galicer, S. Muro, and P. Sevilla-Peris, Asymptotic estimates on the von Neumann inequality for homogeneous polynomials, J. Reine Angew. Math. 743 (2018), 213–227.
  • L. Kaup and B. Kaup, Holomorphic functions of several variables: An introduction to fundamental theory, With the assistance of Gottfried Barthel, Translated from the German by Michael Bridgland, De Gruyter Studies in Mathematics, 3. Walter de Gruyter & Co., Berlin, 1983.
  • A. M. Mantero and A. Tonge, Banach algebras and von Neumann's inequality, Proc. London Math. Soc. (3) 38 (1979), no. 2,309–334.
  • V. Müller, Taylor functional calculus, Alpay, Daniel (ed.), Operator theory, In 2 volumes, Basel: Springer, Springer Reference, 1181–1215 (2015).
  • J. von Neumann, Eine Spektraltheorie für allgemeine Operatoren eines unitären Raumes (German), Math. Nachr. 4 (1951), 258–281.
  • O. Nevanlinna, Lemniscates and $K$-spectral sets, J. Funct. Anal. 262 (2012), no. 4, 1728–1741.
  • O. Nevanlinna, Multicentric holomorphic calculus, Comput. Methods Funct. Theory 12 (2012), no. 1, 45–65.
  • O. Nevanlinna, Polynomial as a new variable - a Banach algebra with a functional calculus, Oper. Matrices 10 (2016), no. 3, 567–592.
  • K. C. O'Meara and C. Vinsonhaler, On approximately simultaneously diagonalizable matrices, Linear Algebra Appl. 412 (2006), no. 1, 39–74.
  • V. Paulsen, Completely bounded maps and operator algebras, Cambridge Studies in Advanced Mathematics, 78. Cambridge University Press, Cambridge, 2002.