caa a22 4500 467931690 CHVBK 20180406152945.0 cr unu---uuuuu 170328e20060601xx s 000 0 eng 10.1007/s00020-005-1382-4 doi (NATIONALLICENCE)springer-10.1007/s00020-005-1382-4 Spectral Shorted Operators [Elektronische Daten] [Jorge Antezana, Gustavo Corach, Demetrio Stojanoff] Abstract.: 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 $$\rho \left( {\mathcal{S},\mathcal{A}} \right)$$ is defined as the infimum of the sequence $$\sum (\mathcal{S},A^n )^{1/n} ,$$ where denotes $$\sum \left( {\mathcal{S},B} \right)$$ the shorted operator of B to $$\mathcal{S}.$$ We characterize the left spectral resolution of $$\rho \left( {\mathcal{S},\mathcal{A}} \right)$$ 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. Birkhäuser Verlag, Basel, 2006 Shorted operator nationallicence spectral order nationallicence positive operators nationallicence spectral resolutions nationallicence Antezana Jorge Departamento de Matemática Facultad de Ciencias Exactas, Universidad Nacional de La Plata, IAM-CONICET, 50 y 115, 1900, La Plata, Argentina aut Corach Gustavo Departamento de Matemática, Facultad de Ingeniería-UBA, IAM-CONICET, Av. Paseo Colón 850 (1063), Buenos Aires, Argentina aut Stojanoff Demetrio Departamento de Matemática Facultad de Ciencias Exactas, Universidad Nacional de La Plata, IAM-CONICET, 50 y 115, 1900, La Plata, Argentina aut Integral Equations and Operator Theory Birkhäuser-Verlag; www.birkhauser.ch 55/2(2006-06-01), 169-188 0378-620X 55:2<169 2006 55 20 https://doi.org/10.1007/s00020-005-1382-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00020-005-1382-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Antezana Jorge Departamento de Matemática Facultad de Ciencias Exactas, Universidad Nacional de La Plata, IAM-CONICET, 50 y 115, 1900, La Plata, Argentina aut NATIONALLICENCE 700 1- Corach Gustavo Departamento de Matemática, Facultad de Ingeniería-UBA, IAM-CONICET, Av. Paseo Colón 850 (1063), Buenos Aires, Argentina aut NATIONALLICENCE 700 1- Stojanoff Demetrio Departamento de Matemática Facultad de Ciencias Exactas, Universidad Nacional de La Plata, IAM-CONICET, 50 y 115, 1900, La Plata, Argentina aut NATIONALLICENCE 773 0- Integral Equations and Operator Theory Birkhäuser-Verlag; www.birkhauser.ch 55/2(2006-06-01), 169-188 0378-620X 55:2<169 2006 55 20 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer