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Universally bounded operators on von Neumann algebras of type II 1

In: Algebraic Methods in Operator Theory

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  • Erik Christensen

    (Københavns Universitet, Matematisk Institut)

Abstract

Continuous linear operators, on a von Neumann algebra M of type II1, with a faithful finite normal trace tr, are called universally bounded if they are bounded with respect to the trace-norm too. The algebra of all universally bounded operators has a natural structure as a Banach *-algebra. As a consequence of Proposition 2.3 we get that this algebra has a natural faithful representation on the Hilbert space L 2(M, tr). Proposition 2.9 show that the Haagerup tensorproduct M sa ⊗ h M sa can be embedded into the algebra of universally bounded operators and Corollary 2.12 show that positive definite functions on discrete groups yield universally bounded operators on the group von Neumann algebra.

Suggested Citation

  • Erik Christensen, 1994. "Universally bounded operators on von Neumann algebras of type II 1," Springer Books, in: Raúl E. Curto & Palle E. T. Jørgensen (ed.), Algebraic Methods in Operator Theory, pages 195-204, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-0255-4_20
    DOI: 10.1007/978-1-4612-0255-4_20
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