Perturbations and operator trace functions

(Pseudo-)Trace Functions and Modular Invariance of Vertex Operator Algebra

By including interlocked modules, we showed a modular invariance property of (pseudo) trace functions of modules for a 2-dimensional conformal field theory satisfying C 2-finiteness condition.

Krein’s Trace Formula for Unitary Operators and Operator Lipschitz Functions

The spectral shift function for pairs of selfadjoint operators was introduced in the paper by I.M. Lifshits [17]. In the same paper a trace formula for the difference of functions of the perturbed operator and the unperturbed operator was established. Ideas by Lifshits were developed in the paper by M.G. Krein [14], in which the spectral shift function ξ in L1(R) was defined for arbitrary pairs...

Some Operator and Trace Function Convexity Theorems

We consider trace functions (A,B) 7→ Tr[(ABA)] where A and B are positive n × n matrices and ask when these functions are convex or concave. We also consider operator convexity/concavity of ABA and convexity/concavity of the closely related trace functional Tr[ABAC]. The concavity questions are completely resolved, thereby settling cases left open by Hiai; the convexity questions are settled in...

Hilbert operator for automorphic L - functions and a local trace formula

A linear operator for symmetric functions and tableaux in a strip with given trace

Goulden, I.P., A linear operator for symmetric functions and tableaux in a strip with given trace, Discrete Mathematics 99 (1992) 69-77. The sum of Schur symmetric functions in a countable set of variables, over partitions with given trace and upper bound on the number of parts, is evaluated. This generalizes results of Gordon (1971). The method is to extend an analogous sum in a finite set of ...