On the Wiener-Hopf compactification of a symmetric cone
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- by S. Sundar PDF
- Proc. Amer. Math. Soc. 145 (2017), 1141-1151 Request permission
Abstract:
Let $V$ be a finite dimensional real Euclidean Jordan algebra with the identity element $1$. Let $Q$ be the closed convex cone of squares. We show that the Wiener-Hopf compactification of $Q$ is the interval $\{x \in V: -1 \leq x \leq 1\}$. As a consequence, we deduce that the $K$-groups of the Wiener-Hopf $C^{*}$-algebra associated to $Q$ are trivial.References
- Alexander Alldridge and Troels Roussau Johansen, Spectrum and analytical indices of the $C^\ast$-algebra of Wiener-Hopf operators, J. Funct. Anal. 249 (2007), no. 2, 425–453. MR 2345339, DOI 10.1016/j.jfa.2007.03.009
- Alexander Alldridge and Troels Roussau Johansen, An index theorem for Wiener-Hopf operators, Adv. Math. 218 (2008), no. 1, 163–201. MR 2409412, DOI 10.1016/j.aim.2007.11.024
- Alexander Alldridge, Convex polytopes and the index of Wiener-Hopf operators, J. Operator Theory 65 (2011), no. 1, 145–155. MR 2765761
- Jacques Faraut and Adam Korányi, Analysis on symmetric cones, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1994. Oxford Science Publications. MR 1446489
- Joachim Hilgert and Karl-Hermann Neeb, Wiener-Hopf operators on ordered homogeneous spaces. I, J. Funct. Anal. 132 (1995), no. 1, 86–118. MR 1346219, DOI 10.1006/jfan.1995.1101
- Paul S. Muhly and Jean N. Renault, $C^{\ast }$-algebras of multivariable Wiener-Hopf operators, Trans. Amer. Math. Soc. 274 (1982), no. 1, 1–44. MR 670916, DOI 10.1090/S0002-9947-1982-0670916-3
- Alexandru Nica, Some remarks on the groupoid approach to Wiener-Hopf operators, J. Operator Theory 18 (1987), no. 1, 163–198. MR 912819
- Jean Renault and S. Sundar, Groupoids associated to Ore semigroup actions, J. Operator Theory 73 (2015), no. 2, 491–514. MR 3346134, DOI 10.7900/jot.2014mar10.2016
- S. Sundar, Toeplitz algebras associated to endomorphisms of Ore semigroups, J. Funct. Anal. 271 (2016), no. 4, 833–882. MR 3507992, DOI 10.1016/j.jfa.2016.05.008
Additional Information
- S. Sundar
- Affiliation: Chennai Mathematical Institute, H1 Sipcot IT Park, Siruseri, Padur, 603103, Tamilnadu, India
- MR Author ID: 906130
- Email: sundarsobers@gmail.com
- Received by editor(s): February 2, 2016
- Received by editor(s) in revised form: May 3, 2016
- Published electronically: September 8, 2016
- Communicated by: Adrian Ioana
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 1141-1151
- MSC (2010): Primary 46L80; Secondary 17CXX
- DOI: https://doi.org/10.1090/proc/13317
- MathSciNet review: 3589314