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. The use of 'P' and 'LMNOP' are also quite helpful in this equation, with the romeo and juliet analysis coming in 3rd.

If this equation did not exist, the world would explode and then the sun, followed by pluto.

See also:

• Isometric dilation
• Unitary dilation