Multilinear maps and tensor norms on operator systems. (English) Zbl 0644.46037

Paulsen, V. I.; Smith, R. R.

J. Funct. Anal. 73, 258-276 (1987).

Authors’ abstract: “We extend work of Christensen and Sinclair on completely bounded multilinear forms to the case of subspaces of C * algebras, and obtain a representation theorem and a Hahn-Banach extension theorem for such maps. In the second part of the paper the Haagerup norms on tensor products are investigated, and we obtain new characterizations of these quantities.”

Reviewer: C.H.Brans

MSC:

46L05	General theory of \(C^*\)-algebras
46M05	Tensor products in functional analysis

Keywords:

completely bounded multilinear forms; subspaces of C * algebras; representation theorem; Hahn-Banach extension theorem; Haagerup norms on tensor products

References:

[1]	Arveson, W.B, Subalgebras of C∗-algebras, Acta math., 123, 141-224, (1969) · Zbl 0194.15701
[2]	Choi, M.-D; Effros, E.G, Injectivity and operator spaces, J. funct. anal., 24, 159-209, (1977) · Zbl 0341.46049
[3]	Christensen, E; Sinclair, A.M, Representations of completely bounded k-linear operators, (1985), preprint
[4]	Effros, E.G, On multilinear completely bounded module maps, (1985), preprint
[5]	Effros, E.G; Kishimoto, A, Module maps and Hochschild-Johnson cohomology, (1985), preprint · Zbl 0635.46062
[6]	Haagerup, U, The Grothendieck inequality for bilinear forms on C∗-algebras, Advan. in math., 56, 93-116, (1985) · Zbl 0593.46052
[7]	Paulsen, V.I, Completely bounded maps on C∗-algebras and invariant operator ranges, (), 91-96 · Zbl 0554.46028
[8]	Paulsen, V.I, Every completely polynomially bounded operator is similar to a contraction, J. funct. anal., 55, 1-17, (1984) · Zbl 0557.46035
[9]	Wittstock, G, Ein operatorwertiger Hahn-Banach satz, J. funct. anal., 40, 127-150, (1981) · Zbl 0495.46005
[10]	Wittstock, G, Extension of completely bounded C∗-module homomorphisms, (1982), preprint · Zbl 0535.46003