Abstract
We characterize smooth points of unit balls in some spaces of
bilinear forms on $\mathbb{R}^2$. We find that for some special
cases of hexagonal norms, the set of smooth points of the unit ball
of symmetric bilinear forms coincides with the set of those smooth
points of the unit ball of bilinear forms that are symmetric.
Надано характеристику гладким точкам одиничних куль в
деяких просторах білінійних форм на $ \mathbb {R}^2$. Знайдено,
що для деяких частинних випадків гексагональних норм множина
гладких точок одиничної кулі співпадає з множиною тих гладких точок
одиничної кулі білінійних форм, які є симетричними.
Key words: Bilinear forms, smooth points, certain hexagonal norms on
$\mathbb{R}^2$.
Full Text
Article Information
| Title | Smooth bilinear forms
of ${\mathcal L}(^2\mathbb{R}_{h(w_1, w_2)}^2)$ and
${\mathcal L}(^2\mathbb{R}_{h^{'}(w_1,
w_2)}^2)$ |
| Source | Methods Funct. Anal. Topology, Vol. 29 (2023), no. 1, 39-56 |
| DOI | 10.31392/MFAT-npu26_1--2.2023.04 |
| Milestones | Received 18/07/2023; Revised 04/03/2024 |
| Copyright | The Author(s) 2023 (CC BY-SA) |
Authors Information
Sung Guen Kim
Department of Mathematics, Kyungpook National University, Daegu 702-701, South Korea
Chang Yeol Lee
Department of Mathematics, Kyungpook National University, Daegu 702-701, South Korea
Citation Example
Sung Guen Kim and Chang Yeol Lee, Smooth bilinear forms
of ${\mathcal L}(^2\mathbb{R}_{h(w_1, w_2)}^2)$ and
${\mathcal L}(^2\mathbb{R}_{h^{'}(w_1,
w_2)}^2)$, Methods Funct. Anal. Topology 29
(2023), no. 1, 39-56.
BibTex
@article {MFAT1910,
AUTHOR = {Sung Guen Kim and Chang Yeol Lee},
TITLE = {Smooth bilinear forms
of ${\mathcal L}(^2\mathbb{R}_{h(w_1, w_2)}^2)$ and
${\mathcal L}(^2\mathbb{R}_{h^{'}(w_1,
w_2)}^2)$},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {29},
YEAR = {2023},
NUMBER = {1},
PAGES = {39-56},
ISSN = {1029-3531},
DOI = {10.31392/MFAT-npu26_1--2.2023.04},
URL = {http://mfat.imath.kiev.ua/article/?id=1910},
}
