Abstract

In this chapter we introduce and study the symbol and Fredholm index of Toeplitz and block Toeplitz operators defined by piecewise continuous functions with a finite number of discontinuities. Sums and products of such operators are also considered. The chapter provides the necessary tools to develop the theory of Banach algebras generated by Toeplitz operators defined by piecewise continuous functions, which will be treated in Chapter XXXII.KeywordsMatrix FunctionCompact OperatorToeplitz OperatorFredholm OperatorMatrix PolynomialThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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