Spectral shorted operators

Details Spectral shorted operators Spectral shorted operators

2004-10-27

arxiv.org/abs/math/0410573v1

Mathematics

Functional Analysis

19 pages

Scientific paper

If $\mathcal H$ is a Hilbert space, $\mathcal S \subseteq \mathcal H$ 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 dimesional case and for non invertible operators.

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