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Volume 27, Issue 4
Projections, Birkhoff Orthogonality and Angles in Normed Spaces

Zhizhi Chen, Wei Lin & Lü-Lin Luo

Commun. Math. Res., 27 (2011), pp. 378-384.

Published online: 2021-05

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  • 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.

  • Keywords

projection, norm, Birkhoff orthogonality, angle, Minkowski plane, duality.

  • AMS Subject Headings

46B20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-27-378, author = {Zhizhi and Chen and and 18429 and and Zhizhi Chen and Wei and Lin and and 18430 and and Wei Lin and Lü-Lin and Luo and and 18431 and and Lü-Lin Luo}, 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. doi:
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