This is an announcement for the paper "Adjoint operators on Banach spaces" by Tepper L Gill, Francis Mensah and Woodford W. Zachary.

Abstract: In this paper, we report on new results related to the existence of an adjoint for operators on separable Banach spaces and discuss a few interesting applications. (Some results are new even for Hilbert spaces.) Our first two applications provide an extension of the Poincar'{e} inequality and the Stone-von Neumann version of the spectral theorem for a large class of $C_0$-generators of contraction semigroups on separable Banach spaces. Our third application provides a natural extension of the Schatten-class of operators to all separable Banach spaces. As a part of this program, we introduce a new class of separable Banach spaces. As a side benefit, these spaces also provide a natural framework for the (rigorous) construction of the path integral as envisioned by Feynman.

Archive classification: math-ph math.FA math.MP

Mathematics Subject Classification: 46B03, 47D03, 47H06, 47F05, 35Q80

Submitted from: tgill@howard.edu

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1010.4922

or

http://arXiv.org/abs/1010.4922