Hostname: page-component-5c6d5d7d68-wp2c8 Total loading time: 0 Render date: 2024-08-16T01:16:13.039Z Has data issue: false hasContentIssue false
  • English
  • Français

APPROXIMATIONS OF SUBHOMOGENEOUS ALGEBRAS

Part of: Linear spaces and algebras of operators Selfadjoint operator algebras Normed linear spaces and Banach spaces; Banach lattices

Published online by Cambridge University Press:  07 February 2019

TATIANA SHULMAN Open the ORCID record for TATIANA SHULMAN [Opens in a new window]  and
OTGONBAYAR UUYE Open the ORCID record for OTGONBAYAR UUYE [Opens in a new window]
TATIANA SHULMAN
Affiliation:
Institute of Mathematics, Polish Academy of Sciences, ul. Śniadeckich 8, 00-656 Warszawa, Poland email tshulman@impan.pl
OTGONBAYAR UUYE*
Affiliation:
Institute of Mathematics, National University of Mongolia, Ikh Surguuliin Gudamj 1, Sukhbaatar District, Ulaanbaatar, Mongolia email otogo@num.edu.mn
*
✉otogo@num.edu.mn
Get access Rights & Permissions [Opens in a new window]

Abstract

Let $n$ be a positive integer. A $C^{\ast }$-algebra is said to be $n$-subhomogeneous if all its irreducible representations have dimension at most $n$. We give various approximation properties characterising $n$-subhomogeneous $C^{\ast }$-algebras.

Keywords

subhomogeneous algebraC∗ -algebrafinite-dimensional algebracompletely positivecompletely contractive

MSC classification

Primary: 46B28: Spaces of operators; tensor products; approximation properties
Secondary: 46L07: Operator spaces and completely bounded maps 47L30: Abstract operator algebras on Hilbert spaces 47L55: Representations of (nonselfadjoint) operator algebras
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 100 , Issue 2 , October 2019 , pp. 328 - 337
Copyright
© 2019 Australian Mathematical Publishing Association Inc. 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

The first author was supported by a Polish National Science Centre grant under the contract number DEC2012/06/A/ST1/00256 and by the grant H2020-MSCA-RISE-2015-691246-QUANTUM DYNAMICS. The second author was supported by Mongolian Science and Technology Foundation grants SSA-012/2016 and ShuSs-2017/76.

References

Blackadar, B., Operator Algebras: Theory of C ∗ -Algebras and von Neumann Algebras, Encyclopaedia of Mathematical Sciences, 122 [Operator Algebras and Non-commutative Geometry III] (Springer, Berlin, 2006).Google Scholar
Brown, N. P. and Ozawa, N., C ∗ -Algebras and Finite-dimensional Approximations, Graduate Studies in Mathematics, 88 (American Mathematical Society, Providence, RI, 2008).Google Scholar
Choi, M. D., ‘Positive linear maps on C ∗ -algebras’, Canad. J. Math. 24 (1972), 520–529.Google Scholar
De Cannière, J. and Haagerup, U., ‘Multipliers of the Fourier algebras of some simple Lie groups and their discrete subgroups’, Amer. J. Math. 107(2) (1985), 455–500.10.2307/2374423Google Scholar
Huruya, T. and Tomiyama, J., ‘Completely bounded maps of C ∗ -algebras’, J. Operator Theory 10(1) (1983), 141–152.Google Scholar
Loebl, R. I., ‘Contractive linear maps on C ∗ -algebras’, Michigan Math. J. 22(4) (1976), 361–366.Google Scholar
Pedersen, G. K., C ∗ -Algebras and Their Automorphism Groups, London Mathematical Society Monographs, 14 (Academic Press [Harcourt Brace Jovanovich], London, 1979).Google Scholar
Smith, R. R., ‘Completely bounded maps between C ∗ -algebras’, J. Lond. Math. Soc. (2) 27(1) (1983), 157–166.10.1112/jlms/s2-27.1.157Google Scholar
Smith, R. R., ‘Completely contractive factorizations of C ∗ -algebras’, J. Funct. Anal. 64(3) (1985), 330–337.Google Scholar
Stinespring, W. F., ‘Positive functions on C ∗ -algebras’, Proc. Amer. Math. Soc. 6 (1955), 211–216.Google Scholar
Takesaki, M., Theory of Operator Algebras. I, Encyclopaedia of Mathematical Sciences, 124 (Springer, Berlin, 2002), reprint of the first (1979) edition.Google Scholar
Tomiyama, J., ‘On the difference of n-positivity and complete positivity in C ∗ -algebras’, J. Funct. Anal. 49(1) (1982), 1–9.Google Scholar
Tomiyama, J. and Takesaki, M., ‘Applications of fibre bundles to the certain class of C ∗ -algebras’, Tôhoku Math. J. (2) 13 (1961), 498–522.Google Scholar
Walter, M. E., ‘Algebraic structures determined by 3 by 3 matrix geometry’, Proc. Amer. Math. Soc. 131(7) (2003), 2129–2131 (electronic).Google Scholar