Linear maps between certain nonseparable 𝐶*-algebras

Huruya, Tadasi

doi:10.1090/S0002-9939-1984-0754701-7

Linear maps between certain nonseparable $C^{\ast }$-algebras
HTML articles powered by AMS MathViewer

by Tadasi Huruya PDF

Proc. Amer. Math. Soc. 92 (1984), 193-197 Request permission

Abstract:

There exists a noninjective commutative ${C^ * }$-algebra $A$ such that every bounded linear map of any ${C^ * }$-algebra into $A$ is decomposed as a linear combination of positive linear maps.

References

Edward G. Effros and E. Christopher Lance, Tensor products of operator algebras, Adv. Math. 25 (1977), no. 1, 1–34. MR 448092, DOI 10.1016/0001-8708(77)90085-8
Tadasi Huruya, Decompositions of completely bounded maps, Acta Sci. Math. (Szeged) 50 (1986), no. 1-2, 183–189. MR 862192
Tadasi Huruya and Jun Tomiyama, Completely bounded maps of $C^{\ast }$-algebras, J. Operator Theory 10 (1983), no. 1, 141–152. MR 715564
H. Elton Lacey, The isometric theory of classical Banach spaces, Die Grundlehren der mathematischen Wissenschaften, Band 208, Springer-Verlag, New York-Heidelberg, 1974. MR 0493279, DOI 10.1007/978-3-642-65762-7
Richard I. Loebl, Contractive linear maps on $C^*$-algebras, Michigan Math. J. 22 (1975), no. 4, 361–366 (1976). MR 397423
Vern I. Paulsen, Completely bounded maps on $C^{\ast }$-algebras and invariant operator ranges, Proc. Amer. Math. Soc. 86 (1982), no. 1, 91–96. MR 663874, DOI 10.1090/S0002-9939-1982-0663874-4
Anthony L. Peressini, Ordered topological vector spaces, Harper & Row, Publishers, New York-London, 1967. MR 0227731
R. R. Smith, Completely bounded maps between $C^{\ast }$-algebras, J. London Math. Soc. (2) 27 (1983), no. 1, 157–166. MR 686514, DOI 10.1112/jlms/s2-27.1.157
Masamichi Takesaki, Theory of operator algebras. I, Springer-Verlag, New York-Heidelberg, 1979. MR 548728, DOI 10.1007/978-1-4612-6188-9

Tensor products and projections of norm one in von Neumann algebras

Recent development of the theory of completely bounded maps between

-algebras

Sze Kai J. Tsui, Decompositions of linear maps, Trans. Amer. Math. Soc. 230 (1977), 87–112. MR 442702, DOI 10.1090/S0002-9947-1977-0442702-9
A. W. Wickstead, Spaces of linear operators between partially ordered Banach spaces, Proc. London Math. Soc. (3) 28 (1974), 141–158. MR 333828, DOI 10.1112/plms/s3-28.1.141
Gerd Wittstock, Ein operatorwertiger Hahn-Banach Satz, J. Functional Analysis 40 (1981), no. 2, 127–150 (German, with English summary). MR 609438, DOI 10.1016/0022-1236(81)90064-1