Compression (functional analysis)

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

PTP

where P 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:

• Isometric dilation
• Unitary dilation

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See also: Compression (functional analysis), Functional analysis, Hilbert space, Invariant subspace, Linear operator, Mathematics, Orthogonal projection, Restriction, Subspace