---
_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. <i>Axioms</i>. 2022;11(5). doi:<a href="https://doi.org/10.3390/axioms11050221">10.3390/axioms11050221</a>
  apa: Glöckner, H. (2022). Aspects of differential calculus related to infinite-dimensional
    vector bundles and Poisson vector spaces. <i>Axioms</i>, <i>11</i>(5). <a href="https://doi.org/10.3390/axioms11050221">https://doi.org/10.3390/axioms11050221</a>
  bibtex: '@article{Glöckner_2022, title={Aspects of differential calculus related
    to infinite-dimensional vector bundles and Poisson vector spaces}, volume={11},
    DOI={<a href="https://doi.org/10.3390/axioms11050221">10.3390/axioms11050221</a>},
    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.” <i>Axioms</i> 11, no. 5 (2022). <a
    href="https://doi.org/10.3390/axioms11050221">https://doi.org/10.3390/axioms11050221</a>.
  ieee: 'H. Glöckner, “Aspects of differential calculus related to infinite-dimensional
    vector bundles and Poisson vector spaces,” <i>Axioms</i>, vol. 11, no. 5, 2022,
    doi: <a href="https://doi.org/10.3390/axioms11050221">10.3390/axioms11050221</a>.'
  mla: Glöckner, Helge. “Aspects of Differential Calculus Related to Infinite-Dimensional
    Vector Bundles and Poisson Vector Spaces.” <i>Axioms</i>, vol. 11, no. 5, 2022,
    doi:<a href="https://doi.org/10.3390/axioms11050221">10.3390/axioms11050221</a>.
  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'
...