Trace class and Lidskii trace formula on Kaplansky - Hilbert modules
Автор: Gnll Uur
Журнал: Владикавказский математический журнал @vmj-ru
Статья в выпуске: 2 т.16, 2014 года.
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In this paper, we introduce and study the concepts of the trace class operators and global eigenvalue of continuous $\Lambda$-linear operators in Kaplansky--Hilbert modules. In particular, we give a variant of Lidskii trace formula for cyclically compact operators in Kaplansky--Hilbert modules.
Kaplansky--hilbert module, cyclically compact operator, global eigenvalue, trace class, lidskii trace formula
Короткий адрес: https://sciup.org/14318458
IDR: 14318458
Список литературы Trace class and Lidskii trace formula on Kaplansky - Hilbert modules
- Ganiev I. G., Kudaybergenov K. K. Measurable bundles of compact operators//Methods Funct. Anal. Topology.-2001.-Vol. 7, № 4.-P. 1-5.
- Kaplansky I. Modules over operator algebras//Amer. J. Math.-1953.-Vol. 75, № 4.-P. 839-858.
- Kudaybergenov K. K., Ganiev I. G. Measurable bundles of compact sets//Uzbek. Mat. Zh.-1999.-№ 6.-P. 37-44.-[in Russian].
- Kudaybergenov K. K. $\nabla$-Fredholm operators in Banach-Kantorovich spaces//Methods Funct. Anal. Topology.-2006.-Vol. 12, № 3.-P. 234-242.
- Kusraev A. G. Boolean valued analysis of duality between universally complete modules//Dokl. Akad. Nauk SSSR.-1982.-Vol. 267, № 5.-P. 1049-1052.
- Kusraev A. G. Vector Duality and Its Applications.-Novosibirsk: Nauka, 1985.-[in Russian].
- Kusraev A. G. On functional representation of type I $AW^\ast$-algebras//Sibirsk. Math. Zh.-1991.-Vol. 32, № 3.-P. 78-88.
- Kusraev A. G. Cyclically Compact Operators in Banach Spaces//Vladikavkaz Math. J.-2000.-Vol. 2, № 1.-P. 10-23.
- Kusraev A. G. Dominated Operators.-Dordrecht etc.: Kluwer Academic Publishers, 2000.
- Wright J. D. M. A spectral theorem for normal operators on a Kaplansky-Hilbert module//Proc. London Math. Soc.-1969.-Vol. 19, № 3.-P. 258-268.
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