On fixed points of self maps of the free ball

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2 Scopus citations

Abstract

In this paper, we study the structure of the fixed point sets of noncommutative self maps of the free ball. We show that for such a map that fixes the origin the fixed point set on every level is the intersection of the ball with a linear subspace. We provide an application for the completely isometric isomorphism problem of multiplier algebras of noncommutative complete Pick spaces.

Original languageEnglish
Pages (from-to)422-441
Number of pages20
JournalJournal of Functional Analysis
Volume275
Issue number2
DOIs
StatePublished - 15 Jul 2018
Externally publishedYes

Keywords

  • Complete Pick spaces
  • Free ball
  • Noncommutative functions
  • Operator algebras

ASJC Scopus subject areas

  • Analysis

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