On a generalization of W*-modules

2009/10/28 by David P. Blecher, Blecher, David P, Jon Kraus +1
Mathematics · #Advanced Operator Algebra Research #Holomorphic and Operator Theory #Advanced Banach Space Theory

paper · pdf · doi:10.48550/arxiv.0910.5404

Abstract

In a recent paper of the first author and Kashyap, a new class of modules over dual operator algebras is introduced. These generalize the W*-modules (that is, Hilbert C*-modules over a von Neumann algebra which satisfy an analogue of the Riesz representation theorem for Hilbert spaces), which in turn generalize the theory of Hilbert spaces. In the present paper we give several new results about these modules.

Citations

• Morita equivalence for c∗-algebras and w∗-algebras
• Morita equivalence of dual operator algebras
• A Morita type equivalence for dual operator algebras

Related

• A characterization and a generalization of W*-modules
• Hilbert H*-modules and Hilbert modules over (non-self-adjoint) operator algebras -- a reference overview II
• Hilbert C*-modules and related subjects - a guided reference overview I
• Hilbert von Neumann modules
• The double commutation theorem for selfdual Hilbert right W*-modules