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- W2799008001 abstract "Abstract This paper contains a further analysis of the Toeplitz-like operators $$T_omega $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>ω</mml:mi> </mml:msub> </mml:math> on $$H^p$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msup> <mml:mi>H</mml:mi> <mml:mi>p</mml:mi> </mml:msup> </mml:math> with rational symbol $$omega $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>ω</mml:mi> </mml:math> having poles on the unit circle that were previously studied in Groenewald (Oper Theory Adv Appl 271:239–268, 2018; Oper Theory Adv Appl 272:133–154, 2019). Here the adjoint operator $$T_omega ^*$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msubsup> <mml:mi>T</mml:mi> <mml:mi>ω</mml:mi> <mml:mo>∗</mml:mo> </mml:msubsup> </mml:math> is described. In the case where $$p=2$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> and $$omega $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>ω</mml:mi> </mml:math> has poles only on the unit circle $${mathbb {T}}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>T</mml:mi> </mml:math> , a description is given for when $$T_omega ^*$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msubsup> <mml:mi>T</mml:mi> <mml:mi>ω</mml:mi> <mml:mo>∗</mml:mo> </mml:msubsup> </mml:math> is symmetric and when $$T_omega ^*$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msubsup> <mml:mi>T</mml:mi> <mml:mi>ω</mml:mi> <mml:mo>∗</mml:mo> </mml:msubsup> </mml:math> admits a selfadjoint extension. If in addition $$omega $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>ω</mml:mi> </mml:math> is proper, it is shown that $$T_omega ^*$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msubsup> <mml:mi>T</mml:mi> <mml:mi>ω</mml:mi> <mml:mo>∗</mml:mo> </mml:msubsup> </mml:math> coincides with the unbounded Toeplitz operator defined by Sarason (Integr Equ Oper Theory 61:281–298, 2008) and studied further by Rosenfeld (Classes of densely defined multiplication and Toeplitz operators with applications to extensions of RKHS’s, 2013; J Math Anal Appl 440:911–921, 2016)." @default.
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- W2799008001 date "2019-09-24" @default.
- W2799008001 modified "2023-10-15" @default.
- W2799008001 title "A Toeplitz-Like Operator with Rational Symbol Having Poles on the Unit Circle III: The Adjoint" @default.
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- W2799008001 doi "https://doi.org/10.1007/s00020-019-2542-2" @default.
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