Invariant Approximation Property for Subgroups

Authors

  • Kankeyanathan Kannan Department of Mathematics and Statistics, Faculty of Science, University of Jaffna, Jaffna

DOI:

https://doi.org/10.26713/cma.v12i3.1519

Keywords:

Uniform Roe algebras, Invariant approximation property, Rapid decay property

Abstract

Analytic properties of invariant approximation property, studies analytic techniques from operator theory that encapsulate geometric properties of a group. We will study the invariant approximation property in various contexts. We shall show that it passes to subgroups.

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References

J. Brodzki, G. A. Niblo and N. Wright, Property A, partial translation structures, and uniform embeddings in groups, Journal of the London Mathematical Society 76(2) (2007), 479 – 497, DOI: 10.1112/jlms/jdm066.

N. P. Brown and N. Ozawa, C¤-Algebras and Finite-Dimensional Approximations, Graduate Studies in Mathematics, Vol. 88, American Mathematical Society, Providence, RI (2008), DOI: 10.1090/gsm/088.

K. R. Davidson, C¤-Algebra by Example, Field Institute Mono-graphs, American Mathematical Society, Providence, RI, Vol. 6 (1986), DOI: 10.1090/fim/006.

U. Haagerup and J. Kraus, Approximation properties for group C¤-algebras and group von Neumann algebras, Transactions of the American Mathematical Society 344(2) (1994), 667 – 699, DOI: 10.2307/2154501.

U. Haagerup, An example of a non nuclear C¤-algebra, which has the metric approximation property, Inventiones Mathematicae 50(3) (1978), 279 – 293, DOI: 10.1007/BF01410082.

P. Jolissaint, Rapidly decreasing functions in reduced C¤-algebras of groups, Trans.Amer. Math. Soc. 317(1) (1990), 167 – 196, https://www.ams.org/journals/tran/1990-317-01/S0002-9947-1990-0943303-2/S0002-9947-1990-0943303-2.pdf.

K. Kannan, The stability properties of strong invariant approximation property, International Journal of Pure and Applied Mathematics 88 (2013), 557 – 567, DOI: 10.12732/ijpam.v88i4.10.

K. Kannan, A discrete Heisenberg group which is not a weakly amenable, International Journal of Mathematical Analysis 8(7) (2014), 317 – 327, DOI: 10.12988/ijma.2014.4123.

J. Roe, Lectures on Coarse Geometry, University Lecture Series, Vol. 31, American Mathematical Society, Providence, RI (2003), DOI: 10.1090/ulect/031.

G. Yu, The coarse Baum-Connes conjecture for spaces which admit a uniform embedding into Hilbert space, Inventiones Mathematicae 139 (2000), 201 – 240, DOI: 10.1007/s002229900032.

J. Zacharias, On the invariant translation approximation property for discrete groups, Proceedings of the American Mathematical Society 134(7) (2006), 1909 – 1916, DOI: 10.1090/S0002-9939-06-08191-3.

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Published

30-09-2021
CITATION

How to Cite

Kannan, K. (2021). Invariant Approximation Property for Subgroups. Communications in Mathematics and Applications, 12(3), 475–481. https://doi.org/10.26713/cma.v12i3.1519

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Section

Research Article