On Unbounded p-Summable Fredholm Modules

✍ Scribed by A.L. Carey; J. Phillips; F.A. Sukochev

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 180 KB
• Volume: 151
• Category: Article
• ISSN: 0001-8708
• DOI: 10.1006/aima.1999.1876

✦ Synopsis

We prove that odd unbounded p-summable Fredholm modules are also bounded p-summable Fredholm modules (this is the odd counterpart of a result of A. Connes for the case of even Fredholm modules). The approach we use is via estimates of the form

an unbounded linear operator affiliated with a semifinite von Neumann algebra M, D&D 0 is a bounded self-adjoint linear operator from M and (1+D 2 0 ) &1Â2 # L p (M, {), where L p (M, {) is a non-commutative L p -space associated with M. It follows from our results that if p # (1, ), then ,(D)&,(D 0 ) belongs to the space L p (M, {). 2000 Academic Press 0. INTRODUCTION This paper concerns the question arising in the quantised calculus of Alain Connes [Co1, Co2] outlined in the abstract. To explain our results we need some further notation. Let M be a semifinite von Neumann algebra on a separable Hilbert space H and let L p (M, {) be a non-commutative