Compression (functional analysis)

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In functional analysis, the compression of a linear operator T on a Hilbert space to a subspace K is the operator

where P_K 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.

See also:

• Dilation