Regularized trace on separable Banach spaces

Abstract

If H is a separable Hilbert space, Gül (2008) has shown that a regularized trace formula can be computed on L² (H, [0, ?]) for a second order differential operator with bounded operator-valued coefficients, where H is a separable Hilbert space. Kuelbs (1970) has shown that every separable Banach space can be continuously and densely embedded into a separable Hilbert space, while Gill (2016) has used Kuelbs result to show that the dual of a Banach space does not have a unique representation. In this paper, we use the results of Kuelbs and Gill to study the regularized trace formula on L2 (B, [0, ?]), where B is an arbitrary separable Banach space.