---
res:
bibo_abstract:
- 'We prove various results in infinite-dimensional differential calculus that relate
the differentiability properties of functions and associated operator-valued functions
(e.g., differentials). The results are applied in two areas: (1) in the theory
of infinite-dimensional vector bundles, to construct new bundles from given ones,
such as dual bundles, topological tensor products, infinite direct sums, and completions
(under suitable hypotheses); (2) in the theory of locally convex Poisson vector
spaces, to prove continuity of the Poisson bracket and continuity of passage from
a function to the associated Hamiltonian vector field. Topological properties
of topological vector spaces are essential for the studies, which allow the hypocontinuity
of bilinear mappings to be exploited. Notably, we encounter kR-spaces and locally
convex spaces E such that E×E is a kR-space.@eng'
bibo_authorlist:
- foaf_Person:
foaf_givenName: Helge
foaf_name: Glöckner, Helge
foaf_surname: Glöckner
foaf_workInfoHomepage: http://www.librecat.org/personId=178
bibo_doi: 10.3390/axioms11050221
bibo_issue: '5'
bibo_volume: 11
dct_date: 2022^xs_gYear
dct_isPartOf:
- http://id.crossref.org/issn/2075-1680
dct_language: eng
dct_title: Aspects of differential calculus related to infinite-dimensional vector
bundles and Poisson vector spaces@
...