2004/10/27 by Jorge Antezana, Antezana, Jorge, Gustavo Corach +3 · 1 citation
Computer Science · Mathematics · #47A30 (Primary) 47B15 (Secondary) #Computability, Logic, AI Algorithms #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math.FA #math.SP #msc:47A30 #msc:47B15
paper · pdf · doi:10.48550/arxiv.math/0410573
19 pages
arxiv created 2004/10/27 · openalex publication_date 2004/10/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
If \mathcal H is a Hilbert space, \mathcal S ⊆ \mathcal H is a closed subspace of \mathcal H, and A is a positive bounded linear operator on \mathcal H, the spectral shorted operator ρ(\mathcal S, A) is defined as the infimum of the sequence Σ(\mathcal S, An)1/n, where Σ(\mathcal S, B) denotes the shorted operator of B to \mathcal S. We characterize the left spectral resolution of ρ(\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.