HighlightsFree radicals can cause significant tissue damage.Scavengers of free radicals are a useful way to reduce reperfusion injury.Electron Paramagnetic Resonance (EPR) spectroscopy is the best way to detect free radicals.
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 Poincaré inequality and the Stone-von Neumann version of the spectral theorem for a large class of C0-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.
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