Abstract
In this paper, we show that the Ritt condition in the case of
locally convex spaces can be related to the power boundedness of a
universally bounded operator. We will characterize this condition by
two geometric properties of the powers and we prove that the Ritt
condition will be shown to be equivalent to the Tadmor condition. We
study the Ritt condition for a quasinilpotent operator acting on
locally convex spaces. Also, an upper bound for the norm of the
powers of operators acting on locally convex spaces under Ritt
condition was given.
Показано, що у випадку локально опуклих просторів умова
Рітта пов’язана з обмеженістю степенів універсально обмеженого
оператора. Ця умова характеризується в термінах геометричних
властивостей степенів. Доведено, що умова Рітта еквівалентна умові
Тедмора. Досліджена умова Рітта для вирадку квазінільпотентних
операторів у локально опуклих просторах. Знайдена також верхня
оцінка норм степенів операторів, які задовольняють умову Рітта.
Key words: Locally convex spaces, universally bounded operator, Ritt resolvent, Tadmor condition, power bounded.
Full Text
Article Information
| Title | On the Ritt condition on Locally Convex Vector Spaces |
| Source | Methods Funct. Anal. Topology, Vol. 27 (2021), no. 1, 10-17 |
| DOI | 10.31392/MFAT-npu26_1.2021.02 |
| MathSciNet |
MR4252993 |
| Milestones | Received 03/05/2020; Revised 04/01/2021 |
| Copyright | The Author(s) 2021 (CC BY-SA) |
Authors Information
Abdellah Akrym
Department of Mathematics, Faculty of Sciences, Chouaib Doukkali University, El Jadida, Morocco
Abdeslam El Bakkali
Department of Mathematics, Faculty of Sciences, Chouaib Doukkali University, El Jadida, Morocco.
Abdelkhalek Faouzi
Department of Mathematics, Faculty of Sciences, Chouaib Doukkali University, El Jadida, Morocco.
Citation Example
Abdellah Akrym, Abdeslam El Bakkali, and Abdelkhalek Faouzi, On the Ritt condition on Locally Convex Vector Spaces, Methods Funct. Anal. Topology 27
(2021), no. 1, 10-17.
BibTex
@article {MFAT1501,
AUTHOR = {Abdellah Akrym and Abdeslam El Bakkali and Abdelkhalek Faouzi},
TITLE = {On the Ritt condition on Locally Convex Vector Spaces},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {27},
YEAR = {2021},
NUMBER = {1},
PAGES = {10-17},
ISSN = {1029-3531},
MRNUMBER = {MR4252993},
DOI = {10.31392/MFAT-npu26_1.2021.02},
URL = {http://mfat.imath.kiev.ua/article/?id=1501},
}
