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   $mathcal H$ is a Hilbert space, $mathcal S$ is a closed subspace of $mathcal H$, and $A $ is a positive bounded linear operator on $mathcal H$,  the spectral shorted operator $ ho(mathcal S,  A)$ is defined as the infimum of the sequence $Sigma (mathcal S, A^n)^{1/n}$, where $Sigma (mathcal S, B)$ denotes the shorted operator of $B$ to $mathcal S$. We characterize the left spectral resolution of $ ho(mathcal S, A)$ and show several properties of this operator, particularly in the case that $dim mathcal S = 1$. We use these results to generalize the concept of Kolmogorov complexity for the infinite dimensional case and for non invertible operators.