Universal C*-algebras defined by completely bounded unital homomorphisms
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| 001 | 605461449 | ||
| 003 | CHVBK | ||
| 005 | 20210128100243.0 | ||
| 007 | cr unu---uuuuu | ||
| 008 | 210128e20151201xx s 000 0 eng | ||
| 024 | 7 | 0 | |a 10.1007/s10114-015-5214-4 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10114-015-5214-4 | ||
| 245 | 0 | 0 | |a Universal C*-algebras defined by completely bounded unital homomorphisms |h [Elektronische Daten] |c [Wen Qian, Don Hadwin] |
| 520 | 3 | |a Suppose A is a unital C*-algebra and r > 1. In this paper, we define a unital C*-algebra C* cb (A, r) and a completely bounded unital homomorphism α r : A → C* cb (A, r) with the property that C* cb (A, r) = C*(α r (A)) and, for every unital C*-algebra B and every unital completely bounded homomorphism φ: A → B, there is a (unique) unital *-homomorphism π: C* cb (A, r) → B such that φ = π ◦ α r . We prove that, if A is generated by a normal set {t λ : λ ∈ Λ}, then C* cb (A, r) is generated by the set {α r (t λ ): λ ∈ Λ}. By proving an equation of the norms of elements in a dense subset of C* cb (A, r) we obtain that, if B is a unital C*-algebra that can be embedded into A, then C* cb (B, r) can be naturally embedded into C* cb (A, r). We give characterizations of C* cb (A, r) for some special situations and we conclude that C* cb (A, r) will be "nice” when dim(A) ≤ 2 and "quite complicated” when dim(A) ≥ 3. We give a characterization of the relation between K-groups of A and K-groups of C* cb (A, r). We also define and study some analogous of C* cb (A, r). | |
| 540 | |a Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg, 2015 | ||
| 690 | 7 | |a Completely bounded unital homomorphisms |2 nationallicence | |
| 690 | 7 | |a universal C*-algebras |2 nationallicence | |
| 690 | 7 | |a K -groups |2 nationallicence | |
| 700 | 1 | |a Qian |D Wen |u Department of Mathematics, East China University of Science and Technology, 200237, Shanghai, P. R. China |4 aut | |
| 700 | 1 | |a Hadwin |D Don |u Department of Mathematics and Statistics, University of New Hampshire, 03824, Durham, NH, USA |4 aut | |
| 773 | 0 | |t Acta Mathematica Sinica, English Series |d Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society |g 31/12(2015-12-01), 1825-1844 |x 1439-8516 |q 31:12<1825 |1 2015 |2 31 |o 10114 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10114-015-5214-4 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10114-015-5214-4 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Qian |D Wen |u Department of Mathematics, East China University of Science and Technology, 200237, Shanghai, P. R. China |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Hadwin |D Don |u Department of Mathematics and Statistics, University of New Hampshire, 03824, Durham, NH, USA |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Acta Mathematica Sinica, English Series |d Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society |g 31/12(2015-12-01), 1825-1844 |x 1439-8516 |q 31:12<1825 |1 2015 |2 31 |o 10114 | ||