Completely bounded maps on 𝐶*-algebras and invariant operator ranges

Paulsen, Vern I.

doi:10.1090/S0002-9939-1982-0663874-4

Completely bounded maps on $C^{\ast }$-algebras and invariant operator ranges
HTML articles powered by AMS MathViewer

by Vern I. Paulsen PDF

Proc. Amer. Math. Soc. 86 (1982), 91-96 Request permission

Abstract:

We give a new proof that every completely bounded map from a ${C^* }$-algebra into $\mathcal {L}(\mathcal {H})$ lies in the linear span of the completely positive maps. In addition, we obtain an equivalent reformulation of the invariant operator range problem.

References

William B. Arveson, Subalgebras of $C^{\ast }$-algebras, Acta Math. 123 (1969), 141–224. MR 253059, DOI 10.1007/BF02392388
John W. Bunce, The similarity problem for representations of $C^{\ast }$-algebras, Proc. Amer. Math. Soc. 81 (1981), no. 3, 409–414. MR 597652, DOI 10.1090/S0002-9939-1981-0597652-0
Erik Christensen, Derivations and their relation to perturbations of operator algebras, Operator algebras and applications, Part 2 (Kingston, Ont., 1980) Proc. Sympos. Pure Math., vol. 38, Amer. Math. Soc., Providence, R.I., 1982, pp. 261–273. MR 679509

Extensions of derivations

Ciprian Foiaş, Invariant para-closed subspaces, Indiana Univ. Math. J. 21 (1971/72), 887–906. MR 293439, DOI 10.1512/iumj.1972.21.21072

Solution of the similarity problem for cyclic representations of

-algebras

D. W. Hadwin, Dilations and Hahn decompositions for linear maps, Canadian J. Math. 33 (1981), no. 4, 826–839. MR 634141, DOI 10.4153/CJM-1981-064-7
Richard V. Kadison, On the orthogonalization of operator representations, Amer. J. Math. 77 (1955), 600–620. MR 72442, DOI 10.2307/2372645
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