Abstract

In this chapter the study of linear mappings between normed linear spaces is begun, with the emphasis being on the case of bounded linear mappings on a Hilbert space. A number of specific examples are given and studied in detail. In the case of a bounded linear mapping on a Hilbert space, the adjoint operator is motivated and defined. Basic properties of the adjoint are established, and many of the earlier examples revisited, in order to determine the corresponding adjoint operator. The significance of the adjoint for solvability of linear operator equations is elaborated, and the notion of a Fredholm operator is presented.

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