Geometric properties of systems of vector states and expansion of states in Pettis integrals
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G. G. Amosov and V. Zh. Sakbaev
Translated by: A. Plotkin - St. Petersburg Math. J. 27 (2016), 589-597
- 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.References
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Bibliographic 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
- 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
- © Copyright 2016 American Mathematical Society
- Journal: St. Petersburg Math. J. 27 (2016), 589-597
- MSC (2010): Primary 46L30
- DOI: https://doi.org/10.1090/spmj/1406
- MathSciNet review: 3580188