---
_id: '34796'
abstract:
- lang: eng
text: '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.'
article_type: original
author:
- first_name: Helge
full_name: Glöckner, Helge
id: '178'
last_name: Glöckner
citation:
ama: Glöckner H. Aspects of differential calculus related to infinite-dimensional
vector bundles and Poisson vector spaces. *Axioms*. 2022;11(5). doi:10.3390/axioms11050221
apa: Glöckner, H. (2022). Aspects of differential calculus related to infinite-dimensional
vector bundles and Poisson vector spaces. *Axioms*, *11*(5). https://doi.org/10.3390/axioms11050221
bibtex: '@article{Glöckner_2022, title={Aspects of differential calculus related
to infinite-dimensional vector bundles and Poisson vector spaces}, volume={11},
DOI={10.3390/axioms11050221},
number={5}, journal={Axioms}, author={Glöckner, Helge}, year={2022} }'
chicago: Glöckner, Helge. “Aspects of Differential Calculus Related to Infinite-Dimensional
Vector Bundles and Poisson Vector Spaces.” *Axioms* 11, no. 5 (2022). https://doi.org/10.3390/axioms11050221.
ieee: 'H. Glöckner, “Aspects of differential calculus related to infinite-dimensional
vector bundles and Poisson vector spaces,” *Axioms*, vol. 11, no. 5, 2022,
doi: 10.3390/axioms11050221.'
mla: Glöckner, Helge. “Aspects of Differential Calculus Related to Infinite-Dimensional
Vector Bundles and Poisson Vector Spaces.” *Axioms*, vol. 11, no. 5, 2022,
doi:10.3390/axioms11050221.
short: H. Glöckner, Axioms 11 (2022).
date_created: 2022-12-21T20:02:29Z
date_updated: 2022-12-22T07:31:55Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
doi: 10.3390/axioms11050221
intvolume: ' 11'
issue: '5'
language:
- iso: eng
publication: Axioms
publication_identifier:
issn:
- 2075-1680
quality_controlled: '1'
status: public
title: Aspects of differential calculus related to infinite-dimensional vector bundles
and Poisson vector spaces
type: journal_article
user_id: '178'
volume: 11
year: '2022'
...