Fredholmness of Band-dominated Operators
In this chapter we introduce a class of operators for which the converse of Corollary 1.3.10 can be proved: if the symbol of the operator is invertible, then the operator is P-Fredholm. The class under consideration consists of band and band-dominated operators which act on l P -spaces over ℝ N . In the forthcoming chapters we will point out that this class is large enough to include, e.g., discretizations of convolution operators and of pseudodifferential operators.
KeywordsBanach Algebra Limit Operator Fredholm Operator Band Operator Special Coefficient
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