Given a cone pseudodifferential operator P we give a full asymptotic expansion as t → 0 of the trace TrPe, where A is an elliptic cone differential operator for which the resolvent exists on a suitable region of the complex plane. Our expansion contains log t and new (log t) terms whose coefficients are given explicitly by means of residue traces. Cone operators are contained in some natural al...

A sufficient condition is obtained for two isometries to be unitarily equivalent. Also, a new class of M-hyponormal operator is constructed

The recently introduced concept of a spectral shift operator is applied in several instances. Explicit applications include Krein's trace formula for pairs of self-adjoint operators, the Birman-Solomyak spectral averaging formula and its operator-valued extension, and an abstract approach to trace formulas based on perturbation theory and the theory of self-adjoint extensions of symmetric opera...

Using a reformulation of the Eichler-Selberg trace formula, due to Frechette, Ono and Papanikolas, we consider the problem of the vanishing (resp. non-vanishing) of traces of Hecke operators on spaces of even weight cusp forms with trivial Nebentypus character. For example, we show that for a fixed operator and weight, the set of levels for which the trace vanishes is effectively computable. Al...

The trace identity of a differential operator deeply reveals the spectral structure of the differential operator and has important applications in the numerical calculation of eigenvalues. Here we refer to the references [2 – 11], with which the author became acquainted while doing research on the present paper. In [12], we obtained regularized trace formula for (1) with the boundary condition

A quantum channel is a completely positive trace preserving map which acts on the set of operators for the Hilbert space associated with a given quantum system. Analysis of such channels is central to quantum computing and quantum information theory. We present and investigate a new class of quantum channels that includes the class of collective rotation channels as a special case. We use the p...