Compression (functional analysis)
where is the orthogonal projection onto K. This is a natural way to obtain an operator on K from an operator on the whole Hilbert space. If K is an invariant subspace for T, then the compression of T to K is the restricted operator K→K sending k to Tk.
More generally, for a linear operator T on a Hilbert space and an isometry V on a subspace of , define the compression of T to by
- P. Halmos, A Hilbert Space Problem Book, Second Edition, Springer-Verlag, 1982.
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