A Criterion for the Existence of the Complete Wave Operators in the Theory of Scattering with Two Spaces
Let K0, K denote two separable Hilbert spaces. The set of bounded linear operators mapping K° into K we denote by R(K0, K). The sets R(K, K0), R(K0), R(K) are defined similarly. When no confusion is possible, we will write simply R. We denote similarly by S1 and Soo the sets of nuclear and completely continuous operators. I0, I denote the identity operators in K0 and K respectively. The symbol s-lim denotes the strong operator limit. If A is a densely defined operator, then D(A) denotes its domain and A* the adjoint operator. We denote by Z the real (spectral) axis.
KeywordsBounded Linear Operator Separable Hilbert Space Local Criterion Consultant Bureau Wave Operator
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