<p>We study the C<InlineEquation ID="IEq22"> <EquationSource Format="TEX">$^*$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mo>∗</mo> </mmultiscripts> </math></EquationSource> </InlineEquation> algebra generated by the composition operator <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$C_a$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>C</mi> <mi>a</mi> </msub> </math></EquationSource> </InlineEquation> acting on the Hardy space <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$H^2$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>H</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation> of the unit disk, given by <InlineEquation ID="IEq25"> <EquationSource Format="TEX">$C_af=f\circ\varphi_a$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>C</mi> <mi>a</mi> </msub> <mi>f</mi> <mo>=</mo> <mi>f</mi> <mo>∘</mo> <msub> <mi>φ</mi> <mi>a</mi> </msub> </mrow> </math></EquationSource> </InlineEquation> , where <Equation ID="Equ1"> <EquationSource Format="TEX">$\varphi_a(z)=\frac{a-z}{1-\bar{a}z},$</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mrow> <msub> <mi>φ</mi> <mi>a</mi> </msub> <mrow> <mo stretchy="false">(</mo> <mi>z</mi> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mi>a</mi> <mo>-</mo> <mi>z</mi> </mrow> <mrow> <mn>1</mn> <mo>-</mo> <mover accent="true"> <mrow> <mi>a</mi> </mrow> <mrow> <mo stretchy="false">¯</mo> </mrow> </mover> <mi>z</mi> </mrow> </mfrac> <mo>,</mo> </mrow> </math></EquationSource> </Equation>for <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$|a|<1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">|</mo> <mi>a</mi> <mo stretchy="false">|</mo> <mo><</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>. Also several operators related to <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$C_a$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>C</mi> <mi>a</mi> </msub> </math></EquationSource> </InlineEquation> are examined.</p>

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

期刊论文
发表日期：

2025年11月24日

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E. Andruchow

摘要

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

The C\(^*\)-algebra of a composition reflection

摘要