caa a22 4500 467932182 CHVBK 20180406152946.0 cr unu---uuuuu 170328e20060401xx s 000 0 eng 10.1007/s00020-005-1370-8 doi (NATIONALLICENCE)springer-10.1007/s00020-005-1370-8 Commutative Sequences of Integrable Functions and Best Approximation With Respect to the Weighted Vector Measure Distance [Elektronische Daten] [L. Raffi, E. Pérez, J. Pérez] Abstract.: Let λ be a countably additive vector measure with values in a separable real Hilbert space H. We define and study a pseudo metric on a Banach lattice of integrable functions related to λ that we call a λ-weighted distance. We compute the best approximation with respect to this distance to elements of the function space by the use of sequences with special geometric properties. The requirements on the sequence of functions are given in terms of a commutation relation between these functions that involves integration with respect to λ. We also compare the approximation that is obtained in this way with the corresponding projection on a particular Hilbert space. Birkhäuser Verlag, Basel, 2006 Vector measures nationallicence integrable function nationallicence best approximation nationallicence Raffi L. Departamento de Matemática Aplicada, E.T.S. Ingenieros de Caminos, Canales y Puertos, Camino de Vera, E-46071, Valencia, Spain aut Pérez E. Departamento de Matemática Aplicada, E.T.S. Ingenieros de Caminos, Canales y Puertos, Camino de Vera, E-46071, Valencia, Spain aut Pérez J. Departamento de Matemática Aplicada, E.T.S. Ingenieros de Caminos, Canales y Puertos, Camino de Vera, E-46071, Valencia, Spain aut Integral Equations and Operator Theory Birkhäuser-Verlag; www.birkhauser.ch 54/4(2006-04-01), 495-510 0378-620X 54:4<495 2006 54 20 https://doi.org/10.1007/s00020-005-1370-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00020-005-1370-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Raffi L. Departamento de Matemática Aplicada, E.T.S. Ingenieros de Caminos, Canales y Puertos, Camino de Vera, E-46071, Valencia, Spain aut NATIONALLICENCE 700 1- Pérez E. Departamento de Matemática Aplicada, E.T.S. Ingenieros de Caminos, Canales y Puertos, Camino de Vera, E-46071, Valencia, Spain aut NATIONALLICENCE 700 1- Pérez J. Departamento de Matemática Aplicada, E.T.S. Ingenieros de Caminos, Canales y Puertos, Camino de Vera, E-46071, Valencia, Spain aut NATIONALLICENCE 773 0- Integral Equations and Operator Theory Birkhäuser-Verlag; www.birkhauser.ch 54/4(2006-04-01), 495-510 0378-620X 54:4<495 2006 54 20 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer