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Fredholm index of Toeplitz pairs with $H^{\infty }$ symbols

Part of: Topological algebras, normed rings and algebras, Banach algebras General theory of linear operators

Published online by Cambridge University Press:  10 December 2024

Penghui Wang Open the ORCID record for Penghui Wang [Opens in a new window]  and
Zeyou Zhu Open the ORCID record for Zeyou Zhu [Opens in a new window]
Penghui Wang
Affiliation:
School of Mathematics, Shandong University, Jinan 250100, Shandong, P. R. China e-mail: phwang@sdu.edu.cn
Zeyou Zhu*
Affiliation:
School of Mathematics, Shandong University, Jinan 250100, Shandong, P. R. China e-mail: phwang@sdu.edu.cn
*
e-mail: 201911795@mail.sdu.edu.cn
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Abstract

In the present paper, we characterize the Fredholmness of Toeplitz pairs on Hardy space over the bidisk with the bounded holomorphic symbols, and hence, we obtain the index formula for such Toeplitz pairs. The key to obtain the Fredholmness of such Toeplitz pairs is the $L^p$ solution of Corona Problem over $\mathbb {D}^2$.

Keywords

Toeplitz pairFredholm indexHardy space over the polydisc

MSC classification

Primary: 47A13: Several-variable operator theory (spectral, Fredholm, etc.)
Secondary: 46H25: Normed modules and Banach modules, topological modules (if not placed in or )

Information

Type
Article
Information
Canadian Mathematical Bulletin , Volume 68 , Issue 1 , March 2025 , pp. 166 - 176
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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Footnotes

This work is supported by NSFC: (12271298 and 11871308).

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