## REGULARIZED TRACE ON SEPARABLE BANACH SPACES

## REGULARIZED TRACE ON SEPARABLE BANACH SPACES

*E. Gül, T. L. Gill*

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## Abstract

If H is a separable Hilbert space, Gul (2008) has shown that a regularized trace formula can be computed on L2(H; [0; ]) for a second order di erential operator with bounded operator-valued coe cients, 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.

## Keywords

Dual space, adjoint operator, Schatten classes, regularized trace formula.