The Central Haagerup Tensor Product and Maps between von Neumann Algebras

✍ Scribed by A. Chatterjee; R.R. Smith

• Publisher: Elsevier Science
• Year: 1993
• Tongue: English
• Weight: 754 KB
• Volume: 112
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.1993.1027

✦ Synopsis

We introduce the central Haagerup tensor product (\mathscr{A} \otimes{ }_{g h}), for a von Neumann algebra (\mathscr{A}). and we show that the natural injection into the space (C B(\mathscr{A}, \mathscr{A})) of completely bounded maps on (h) is isometric. This is used to study mappings between von Neumann algebras and to give a new characterization of injectivity. This tensor product is also studied for (C^{*})-algebras (\alpha), and we show that the injection into (C B(, \mathscr{N}, \mathcal{C})) need not always be isometric. depending on the topology of the primilive ideal space of . (\alpha). ' 1993 Academic Press. Inc