Projections, Birkhoff Orthogonality and Angles in Normed Spaces
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@Article{CMR-27-378,
author = {Chen , ZhizhiLin , Wei and Luo , Lü-Lin},
title = {Projections, Birkhoff Orthogonality and Angles in Normed Spaces},
journal = {Communications in Mathematical Research },
year = {2021},
volume = {27},
number = {4},
pages = {378--384},
abstract = {
Let $X$ be a Minkowski plane, i.e., a real two dimensional normed linear space. We use projections to give a definition of the angle $A_q(x, y)$ between two vectors $x$ and $y$ in $X$, such that $x$ is Birkhoff orthogonal to $y$ if and only if $A_q(x, y) = \frac{π}{2}$. Some other properties of this angle are also discussed.
}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19081.html} }
TY - JOUR
T1 - Projections, Birkhoff Orthogonality and Angles in Normed Spaces
AU - Chen , Zhizhi
AU - Lin , Wei
AU - Luo , Lü-Lin
JO - Communications in Mathematical Research
VL - 4
SP - 378
EP - 384
PY - 2021
DA - 2021/05
SN - 27
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/cmr/19081.html
KW - projection, norm, Birkhoff orthogonality, angle, Minkowski plane, duality.
AB -
Let $X$ be a Minkowski plane, i.e., a real two dimensional normed linear space. We use projections to give a definition of the angle $A_q(x, y)$ between two vectors $x$ and $y$ in $X$, such that $x$ is Birkhoff orthogonal to $y$ if and only if $A_q(x, y) = \frac{π}{2}$. Some other properties of this angle are also discussed.
Zhizhi Chen, Wei Lin & Lü-Lin Luo. (2021). Projections, Birkhoff Orthogonality and Angles in Normed Spaces.
Communications in Mathematical Research . 27 (4).
378-384.
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