Trace class and Lidskii trace formula on Kaplansky-Hilbert modules

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Home Editorial board Publication ethics Peer review guidelines Latest issue All issues Rules for authors Online submission system's guidelines Submit manuscript Contacts Address: Vatutina st. 53, Vladikavkaz, 362025, RNO-A, Russia Phone: (8672)23-00-54 E-mail: rio@smath.ru	DOI: 10.23671/VNC.2016.2.7386 Trace class and Lidskii trace formula on Kaplansky-Hilbert modules Gonullu U. Vladikavkaz Mathematical Journal 2014. Vol. 16. Issue 2. Abstract: 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. Keywords: Kaplansky-Hilbert module, cyclically compact operator, global eigenvalue, trace class, Lidskii trace formula. Language: English Download the full text For citation: Gonullu U. Trace class and Lidskii trace formula on Kaplansky-Hilbert modules. Vladikavkazskii matematicheskii zhurnal [Vladikavkaz Math. J.], vol. 16, no. 2, pp.29-37. DOI 10.23671/VNC.2016.2.7386 + References 1. Ganiev I. G., Kudaybergenov K. K. Measurable bundles of compact operators. Methods Funct. Anal. Topology, 2001, vol. 7, no. 4, pp. 1-5. 2. Kaplansky I. Modules over operator algebras. Amer. J. Math, 1953, vol. 75, no. 4, pp. 839-858. 3. Kudaybergenov K. K., Ganiev I. G. Measurable bundles of compact sets. Uzbek. Mat. Zh., 1999, no. 6, pp. 37-44 (Russian). 4. Kudaybergenov K. K. nabla-Fredholm operators in Banach - Kantorovich spaces. Methods Funct. Anal. Topology, 2006, vol. 12, no. 3, pp. 234-242. 5. Kusraev A. G. Boolean valued analysis of duality between universally complete modules. Dokl. Akad. Nauk SSSR, 1982, vol. 267, no. 5, pp. 1049-1052. 6. Kusraev A. G. Vector Duality and Its Applications, Novosibirsk, Nauka, 1985 (Russian). 7. Kusraev A. G. On functional representation of type I AW-algebras. Sibirsk. Math. Zh., 1991, vol. 32, no. 3, pp. 78-88. 8. Kusraev A. G. Cyclically Compact Operators in Banach Spaces. Vladikavkaz Math. J., 2000, vol. 2, no. 1, pp. 10-23. 9. Kusraev A. G. Dominated Operators, Dordrecht etc., Kluwer Academic Publishers, 2000. 10. Wright J. D. M. A spectral theorem for normal operators on a Kaplansky - Hilbert module. Proc. London Math. Soc.*, 1969, vol. 19, no. 3, pp. 258-268. The sole copyright holder of the published work is the Founder of the Vladikavkaz Mathematical Journal. The terms of use of this work are governed by an open license (Creative Commons Attribution-NonCommercial 4.0 International). The use of metadata of the scientific article, including the title, abstract, author information, references, identifiers, and other bibliographic description elements for subsequent unrestricted use, is carried out under the terms of the CC BY or CC0 open licenses. ← Contents of issue


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