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 αr：A → C（cb）＊（A,r）with the property that C（cb）＊（A,r）=C...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 αr：A → C（cb）＊（A,r）with the property that C（cb）＊（A,r）=C＊（αr（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 thatφ=πoαr.We prove that,if A is generated by a normal set {tλ：λ∈Λ},then C（cb）＊（A,r）is generated by the set {αr（tλ）：λ∈Λ}.By proving an equation of the norms of elements in a dense subset of C（cb）＊（A,r）we obtain that,if Β 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）.展开更多
基金partially supported by a Collaboration Grant from the Simons Foundation
文摘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 αr：A → C（cb）＊（A,r）with the property that C（cb）＊（A,r）=C＊（αr（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 thatφ=πoαr.We prove that,if A is generated by a normal set {tλ：λ∈Λ},then C（cb）＊（A,r）is generated by the set {αr（tλ）：λ∈Λ}.By proving an equation of the norms of elements in a dense subset of C（cb）＊（A,r）we obtain that,if Β 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）.
