One sided invertibility of matrices over commutative rings, corona problems, and Toeplitz operators with matrix symbols
Abstract
Conditions are established under which Fredholmness, Coburn's property and one- or two-sided invertibility are shared by a Toeplitz operator with matrix symbol G and the Toeplitz operator with scalar symbol G. These results are based on one-sided invertibility criteria for rectangular matrices over appropriate commutative rings and related scalar corona type problems.
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