The C$^*$-algebra of a composition reflection

We study the C$^*$ algebra generated by the composition operator $C_a$ acting on the Hardy space $H^2$ of the unit disk, given by $C_af=f\circ\varphi_a$, where $$ \varphi_a(z)=\frac{a-z}{1-\bar{a}z}, $$ for $|a|<1$. Also several operators related to $C_a$ are examined.

Publication Details

Journal
ArXiv.org
Published
2025-04-15
Primary Topic
Holomorphic and Operator Theory
Type
article
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article

The C$^*$-algebra of a composition reflection

ArXiv.org
Holomorphic and Operator Theory
article

The C$^*$-algebra of a composition reflection

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Abstract

We study the C$^*$ algebra generated by the composition operator $C_a$ acting on the Hardy space $H^2$ of the unit disk, given by $C_af=f\circ\varphi_a$, where $$ \varphi_a(z)=\frac{a-z}{1-\bar{a}z}, $$ for $|a|<1$. Also several operators related to $C_a$ are examined.

ArXiv.org
Reduced inequalities
Openalex Percentile: Top 38%
Holomorphic and Operator Theory
Open Access PDFOpenAlex
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The C$^*$-algebra of a composition reflection · ArXiv.org (2025) | TGRS Research Map | TGRS