Spectral shorted operators

J. ANTEZANA, G. CORACH Y D. STOJANOFF

INTEGRAL EQUATIONS AND OPERATOR THEORY

Birkhauser

Año: 2006 vol. 55 p. 169 - 188

0378-620X

If H is a Hilbert space, S is a closed subspace of H, and A is apositive bounded linear operator on H, the spectral shorted operator ñ(S,A)is defined as the infimum of the sequence Ó(S,A_n)^1/n, where Ó(S,B) denotesthe shorted operator of B to S. We characterize the left spectral resolution ofñ(S,A) and show several properties of this operator, particularly in the casethat dim S = 1. We use these results to generalize the concept of Kolmogorovcomplexity for the infinite dimensional case and for non invertible operators.