On fixed points of self maps of the free ball

Eli Shamovich

doi:10.1016/j.jfa.2018.03.004

On fixed points of self maps of the free ball

Eli Shamovich

Research output: Contribution to journal › Article › peer-review

3 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 language	English
Pages (from-to)	422-441
Number of pages	20
Journal	Journal of Functional Analysis
Volume	275
Issue number	2
DOIs	https://doi.org/10.1016/j.jfa.2018.03.004
State	Published - 15 Jul 2018
Externally published	Yes

Keywords

Complete Pick spaces
Free ball
Noncommutative functions
Operator algebras

ASJC Scopus subject areas

Analysis

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10.1016/j.jfa.2018.03.004

Cite this

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title = "On fixed points of self maps of the free ball",

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.",

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author = "Eli Shamovich",

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AB - 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.

KW - Complete Pick spaces

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KW - Noncommutative functions

KW - Operator algebras

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On fixed points of self maps of the free ball

Abstract

Keywords

ASJC Scopus subject areas

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