Journal of Operator Theory

Volume 58, Issue 2, Fall 2007 pp. 251-268.

Defect operators and Fredholmness for Toeplitz pairs with inner symbols

Authors: Kunyu Guo (1) and Penghui Wang (2)
Author institution: (1) School of Mathematical Sciences, Fudan University, Shanghai, 200433, P. R. China
(2) Institute of Systems Science, Chinese Academy of Sciences, Beijing 100080, P. R. China

Summary: In this paper, we study defect operators and Fredholmness for Toeplitz pairs with inner symbols on both the Hardy spaces

$H^2\!(\mathbb{D})$ and

$H^2\!({\mathbb{D}}^2)$ . The defect operator theory is closely related to function theory on the unit disk and the bidisk. Fredholmness of Toeplitz pairs on

$\hr$ with rational inner symbols is completely characterized. We also establish an index formula for a general isometric pair.

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