Abstract and Applied Analysis

A Few Conditions for a C * -Algebra to Be Commutative

Lajos Molnár

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Abstract

We present a few characterizations of the commutativity of C * -algebras in terms of particular algebraic properties of power functions, the logarithmic and exponential functions, and the sine and cosine functions.

Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 705836, 4 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412276993

Digital Object Identifier
doi:10.1155/2014/705836

Mathematical Reviews number (MathSciNet)
MR3212443

Zentralblatt MATH identifier
07022915

Citation

Molnár, Lajos. A Few Conditions for a ${C}^{\ast}$ -Algebra to Be Commutative. Abstr. Appl. Anal. 2014 (2014), Article ID 705836, 4 pages. doi:10.1155/2014/705836. https://projecteuclid.org/euclid.aaa/1412276993


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References

  • L. Molnár, “Jordan triple endomorphisms and isometries of unitary groups,” Linear Algebra and its Applications, vol. 439, no. 11, pp. 3518–3531, 2013.
  • L. Molnár, “Jordan triple endomorpisms and isometries of spa-ces of positive definite matrices,” Linear and Multilinear Algebra, 2013.
  • L. Molnár, “General Mazur-Ulam type theorems and some ap-plications,” to appear in Operator Theory: Advances and Applications.
  • M. J. Crabb, J. Duncan, and C. M. McGregor, “Characterizations of commutativity for ${C}^{\ast\,\!}$-algebras,” Glasgow Mathematical Journal, vol. 15, pp. 172–175, 1974.
  • G. Ji and J. Tomiyama, “On characterizations of commutativity of ${C}^{\ast\,\!}$-algebras,” Proceedings of the American Mathematical Society, vol. 131, no. 12, pp. 3845–3849, 2003.
  • T. Ogasawara, “A theorem on operator algebras,” Journal of Sci-ence Hiroshima University A, vol. 18, pp. 307–309, 1955.
  • S. Sherman, “Order in operator algebras,” American Journal of Mathematics, vol. 73, pp. 227–232, 1951.
  • W. Wu, “An order characterization of commutativity for ${C}^{\ast\,\!}$-algebras,” Proceedings of the American Mathematical Society, vol. 129, no. 4, pp. 983–987, 2001.
  • J.-S. Jeang and C.-C. Ko, “On the commutativity of ${C}^{\ast\,\!}$-algebras,” Manuscripta Mathematica, vol. 115, no. 2, pp. 195–198, 2004.
  • R. Beneduci and L. Molnár, “On the standard K-loop structure of positive invertible elements in a ${C}^{\ast\,\!}$- algebra,” to appear in Journal of Mathematical Analysis and Applications. \endinput