Universally bounded operators on von Neumann algebras of type II 1

Erik Christensen
Additional contact information
Erik Christensen: Københavns Universitet, Matematisk Institut

A chapter in Algebraic Methods in Operator Theory, 1994, pp 195-204 from Springer

Abstract: 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.

Keywords: Continuous Linear Operator; Positive Definite Function; Hochschild Cohomology; Finite Algebra; Left Regular Representation (search for similar items in EconPapers)
Date: 1994
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-0255-4_20

Ordering information: This item can be ordered from
http://www.springer.com/9781461202554

DOI: 10.1007/978-1-4612-0255-4_20

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().