Geodesic
Fredholm index of Toeplitz pairs with $H^{\infty }$ symbols
Canadian mathematical bulletin, Tome 68 (2025) no. 1, pp. 166-176

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DOI

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 $\mathbb {D}^2$.
DOI : 10.4153/S0008439524000754
Mots-clés : Toeplitz pair, Fredholm index, Hardy space over the polydisc 
Wang, Penghui; Zhu, Zeyou. Fredholm index of Toeplitz pairs with $H^{\infty }$ symbols. Canadian mathematical bulletin, Tome 68 (2025) no. 1, pp. 166-176. doi: 10.4153/S0008439524000754
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     title = {Fredholm index of {Toeplitz} pairs with $H^{\infty }$ symbols},
     journal = {Canadian mathematical bulletin},
     pages = {166--176},
     year = {2025},
     volume = {68},
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     doi = {10.4153/S0008439524000754},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439524000754/}
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