caa a22 4500 475741293 CHVBK 20180406123500.0 cr unu---uuuuu 170329e20000101xx s 000 0 eng 10.1007/BF02675795 doi (NATIONALLICENCE)springer-10.1007/BF02675795 Mukhamedov F. V. I. Romanovskii Mathematics Institute of the Republic of Uzbekistan, Tashkent aut On the Blum-Hanson theorem for quantum quadratic processes [Elektronische Daten] [F. Mukhamedov] In this paper an analog of the Blum-Hanson theorem for quantum quadratic processes on the von Neumann algebra is proved, i.e., it is established that the following conditions are equivalent: i) P( t )x is weakly convergent tox 0; ii) for any sequence {a n} of nonnegative integrable functions on [1, ∞) such that ∝ 1 ∞ a n(t)dt=1 for anyn and lim n→∞ ∥a n∥∞=0, the integral ∝ 1 ∞ a n(t)P( t )x dt is strongly convergent tox 0 inL 2(M, ϕ), wherex ɛM,P( t ) is a quantum quadratic process,M is a von Neumann algebra, andϕ is an exact normal state onM. Kluwer Academic/Plenum Publishers, 2000 quantum quadratic stochastic process nationallicence Blum-Hanson theorem nationallicence von Neumann algebra nationallicence Mendel model nationallicence genotype nationallicence finite measure space nationallicence Hilbert space nationallicence Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 67/1(2000-01-01), 81-86 0001-4346 67:1<81 2000 67 11006 https://doi.org/10.1007/BF02675795 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02675795 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Mukhamedov F. V. I. Romanovskii Mathematics Institute of the Republic of Uzbekistan, Tashkent aut NATIONALLICENCE 773 0- Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 67/1(2000-01-01), 81-86 0001-4346 67:1<81 2000 67 11006 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer