Spectral flow and Dixmier traces

We obtain general theorems which enable the calculation of the Dixmier trace in terms of the asymptotics of the zeta function and of the heat operator in a general semi-finite von Neumann algebra. Our results have several applications. We deduce a formula for the Chern character of an odd ${\mathcal L}^{(1,\infty)}$-summable Breuer-Fredholm module in terms of a Hochschild 1-cycle. We explain how to derive a Wodzicki residue for pseudo-differential operators along the orbits of an ergodic \IR^n action on a compact space $X$. Finally we give a short proof an index theorem of Lesch for generalised Toeplitz operators

Accounting Profession\u27s New Opportunity, Text of an Address Presented February 27, 1945, at a Meeting of the Philadelphia Chapter of the Pennsylvania Institute of Certified Public Accountants

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