2010/10/24 by Tepper L Gill, Tepper L. Gill, Francis Mensah +5 · 1 citation
Mathematics · Physics and Astronomy · #35Q80 #46B03 #47D03 #47F05 #47H06 #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Functional Equations Stability Results #Mathematical Analysis and Transform Methods #Mathematical Physics (math-ph) #advanced mathematical theories #math-ph #math.FA #math.MP #msc:35Q80 #msc:46B03 #msc:47D03 #msc:47F05 #msc:47H06
paper · pdf · doi:10.48550/arxiv.1010.4922
arxiv created 2010/10/24 · openalex publication_date 2010/10/24 · arxiv updated 2010/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.