We construct a theory of Banach spaces of “generalized” operators with bounded projection trace over a given Hilbert space. This theory can be efficient in the investigation of evolution problems for quantum systems with infinitely many particles.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
C. Cercignani, V. I. Gerasimenko, and D. Ya. Petrina, Many-Particle Dynamics and Kinetic Equations, Kluwer, Dordrecht (1997).
A. Arnold, “Mathematical properties of quantum evolution equations,” Lect. Notes Math., 1946, 45–109 (2008).
V. I. Gerasimenko, “Groups of operators for evolution equations of quantum many-particle systems,” Oper. Theory: Adv. Appl., 191, 341–355 (2009).
Ya. I. Grushka, “Spaces of operators with bounded projection trace,” Mat. Visn. Nauk. Tov. Im. Shevchenka, 6, 73–86 (2009).
D. Ya. Petrina, Mathematical Foundations of Quantum Statistical Mechanics. Continuous Systems, Kluwer, Dordrecht (1995).
L. D. Kudryavtsev, A Course in Mathematical Analysis [in Russian], Vol. 2, Vysshaya Shkola, Moscow (1981).
R. M. Dudley, “On sequential convergence,” Trans. Amer. Math. Soc., 112, No. 3, 483–507 (1964).
V. V. Mosyagin and B. M. Shirokov, “Linear spaces with convergence and a cone,” Tr. Petrozavodsk. Gos. Univ., Ser. Mat., Issue 8, 14–19 (2001).
Yu. M. Berezanskii and Yu. G. Kondrat’ev, Spectral Methods in Infinite-Dimensional Analysis [in Russian], Naukova Dumka, Kiev (1988).
V. I. Gorbachuk and M. L. Gorbachuk, Boundary-Value Problems for Operator Differential Equations [in Russian], Naukova Dumka, Kiev (1984).
V. I. Gorbachuk and M. L. Gorbachuk, “Trigonometric series and generalized periodic functions,” Dokl. Akad. Nauk SSSR, 257, No. 4, 799–804 (1981).
Ya. I. Grushka, “Translation-invariant operators and an operator analog of the trace with respect to a difference variable,” Dopov. Nats. Akad. Nauk Ukr., No. 3, 13–18 (2010).
A. Michelangeli, Bose–Einstein Condensation: Analysis of Problems and Rigorous Results, S.I.S.S.A. Preprint 70/2007/mp.
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 1, pp. 24–39, January, 2011.
About this article
Cite this article
Grushka, Y.I. Spaces of generalized operators with bounded projection trace. Ukr Math J 63, 27 (2011). https://doi.org/10.1007/s11253-011-0486-z
- Linear Space
- Generalize Operator
- Spectral Measure
- Difference Variable
- Linear Normed Space