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Geometric properties of systems of vector states and expansion of states in Pettis integrals


Authors: G. G. Amosov and V. Zh. Sakbaev
Translated by: A. Plotkin
Original publication: Algebra i Analiz, tom 27 (2015), nomer 4.
Journal: St. Petersburg Math. J. 27 (2016), 589-597
MSC (2010): Primary 46L30
DOI: https://doi.org/10.1090/spmj/1406
Published electronically: June 2, 2016
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Abstract: The relationship is studied between the geometry ofsystems unit vectors in Hilbert space and the state on the algebra of bounded operators that is obtained by integration of the vector states determined by the system in question with respect to a finitely additive measure on the set of natural numbers.


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Additional Information

G. G. Amosov
Affiliation: Steklov Mathematical institute, Russian Academy of Sciences, 9 Gubkin str., 119991 Moscow, Russia; St.-Petersburg state university, 7–9 Universitetskaya nab., 199034 St.-Petersburg, Russia; Moscow physicotechnical institute, 9 Institutskiĭ per., 141700 Dolgoprudnyĭ, Russia
Email: gramos@mi.ras.ru

V. Zh. Sakbaev
Affiliation: Moscow physicotechnical institute, 9 Institutskiĭ per., 141700 Dolgoprudnyĭ, Russia
Email: fumi2003@mail.ru

DOI: https://doi.org/10.1090/spmj/1406
Keywords: Finitely additive measure, ultrafilter, Pettis integral, state on the algebra of bounded operators
Received by editor(s): May 23, 2014
Published electronically: June 2, 2016
Additional Notes: Work of the second author was supported by RNF grant no. 14-11-00687
Article copyright: © Copyright 2016 American Mathematical Society