caa a22 4500 605461449 CHVBK 20210128100243.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s10114-015-5214-4 doi (NATIONALLICENCE)springer-10.1007/s10114-015-5214-4 Universal C*-algebras defined by completely bounded unital homomorphisms [Elektronische Daten] [Wen Qian, Don Hadwin] 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). Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg, 2015 Completely bounded unital homomorphisms nationallicence universal C*-algebras nationallicence K -groups nationallicence Qian Wen Department of Mathematics, East China University of Science and Technology, 200237, Shanghai, P. R. China aut Hadwin Don Department of Mathematics and Statistics, University of New Hampshire, 03824, Durham, NH, USA aut Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/12(2015-12-01), 1825-1844 1439-8516 31:12<1825 2015 31 10114 https://doi.org/10.1007/s10114-015-5214-4 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10114-015-5214-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Qian Wen Department of Mathematics, East China University of Science and Technology, 200237, Shanghai, P. R. China aut NATIONALLICENCE 700 1- Hadwin Don Department of Mathematics and Statistics, University of New Hampshire, 03824, Durham, NH, USA aut NATIONALLICENCE 773 0- Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/12(2015-12-01), 1825-1844 1439-8516 31:12<1825 2015 31 10114