Trace Formula in Two Variables

Date: 
Thursday, October 10, 2013 - 3:30pm
Location: 
MSB 111
Speaker: 
Kalyan B. Sinha (J.N. Centre for Advanced Scientific Research,Bangalore, India)

Krein's theorem for a pair of self-adjoint operators , differing by a trace-class operator, was proven by using finite-dimensional approximations by Voiculescu and by Mohapatra and Sinha. Later the same method was extended by Chattopadhyay and Sinha for higher order trace formulae in one operator variable . A similar finite-dimensional approximation scheme is proven for a pair of commuting tuples of self-adjoint operators, differing by Hilbert-Schmidt class. This is used to derive a Stokes' theorem-like trace formula for the pair of commuting tuples.

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