Abstract
Let denote a Hilbert space (real or complex), with inner product (|). In order to present our notation, we recall that if is a vector subspace of (and ‘vector sub-spaces’ will always be closed), with orthocomplement , a partial isometry V with initial domain is a linear operator in which preserves length, and so inner-product, in and is zero in is the final domain of V, and it is easy to verify that V*, the adjoint operator, is also a partial isometry, with initial domain and final domain .
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