Previous issue ·  Next issue ·  Most recent issue · All issues   
Home Overview Authors Editorial Contact Subscribe

Journal of Operator Theory

Volume 35, Issue 1, Winter 1996  pp. 179-189.

A remark on trace properties of K-cycles

Authors:  Fabio Cipriani (1), Daniele Guido (2) and Sergio Scarlatti (3)
Author institution: (1) Mathematical Department, University of Nottingham, University Park NG7-2RD, Nottingham, UNITED KINGDOM
(2) Dipartimento di Matematica, Universita di Roma “Tor Vergata”, Via della Ricerca Scientifica, I-00133 Roma, ITALIA
(3) Dipartimento di Matematica, Universita di Roma “Tor Vergata”, Via della Ricerca Scientifica, I-00133 Roma, ITALIA

Summary:  In this paper we discuss trace properties of d^+-summable K-cycles considered by A. Connes in [6]. More precisely we give a proof of a trace theorem on the algebra $\mathcal A$ of a K-cycle stated in [6], namely we show that a natural functional on $\mathcal A$ is a trace functional. Then we discuss whether this functional gives a trace on the whole universal graded differential algebra $\Omega(\mathcal A)$. On the one hand we prove that the regularity conditions on K-cycles considered in [6] imply the trace property on $\Omega(\mathcal A)$. On the other hand, by constructing an explicit counterexample, we remark that the sole K-cycle assumption is not sufficient for such a property to hold.


Contents    Full-Text PDF