Some recent work in Frechet geometry

2011/09/20 by Christopher T. J. Dodson, Dodson, C. T. J.
Mathematics · #47A16 #47B37 #58A05 #58B25 #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Holomorphic and Operator Theory #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1109.4241

openalex publication_date 2011/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Some recent work in Frechet geometry is briefly reviewed. In particular an earlier result on the structure of second tangent bundles in the finite dimensional case was extended to infinite dimensional Banach manifolds and Frechet manifolds that could be represented as projective limits of Banach manifolds. This led to further results concerning the characterization of second tangent bundles and differential equations in the more general Frechet structure needed for applications. A summary is given of recent results on hypercyclicity of operators on Frechet spaces.

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