Spectral shorted operators

J. ANTEZANA; G. CORACH; D. STOJANOFF

INTEGRAL EQUATIONS AND OPERATOR THEORY

BIRKHAUSER VERLAG AG

Lugar: BASEL; Año: 2006 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 $\rho(\mathcal S, A)$ 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 $\rho(\mathcal S, A)$ 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.