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	Dear authors! Submission of all materials is carried out only electronically through Online Submission System in personal account. 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. ← Contents of issue


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