THE DUAL OF THE HAAGERUP TENSOR PRODUCT Academic Article

abstract

• The weak*-Haagerup tensor product of two von Neumann algebras is related to the Haagerup tensor product in the same way that the von Neumann algebra tensor product is related to the spatial tensor product. Many of the fundamental theorems about completely bounded multilinear maps may be deduced from elementary properties of the weak*-Haagerup tensor product. We show that X* (r)w.h Y* = (X h Y)* for all operator spaces X and Y. The weak*-Haagerup tensor product has simple characterizations and behaviour with reference to slice map properties. The tensor product of two (not necessarily self-adjoint) operator algebras is proven to have many strong commutant properties. All operator spaces possess a certain approximation property which is related to this tensor product. The connection between bimodule maps and commutants is explored. 1992 Oxford University Press.

authors

• Smith, Roger

published proceedings

• JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES

author list (cited authors)

• BLECHER, D. P., & SMITH, R. R.

citation count

• 40

complete list of authors

• BLECHER, DP||SMITH, RR

publication date

• January 1992

publisher

• Wiley  Publisher

published in

• Journal of London Mathematical Society  Journal

Digital Object Identifier (DOI)

• 10.1112/jlms/s2-45.1.126

start page

• 126

end page

• 144

volume

• 45

issue

• 1

URL

• http%3A%2F%2Fdx.doi.org%2F10.1112%2Fjlms%2Fs2-45.1.126