TY - JOUR ID - 29391 TI - Projection Inequalities and Their Linear Preservers JO - Wavelet and Linear Algebra JA - WALA LA - en SN - 2383-1936 AU - Jamshidi, Mina AU - Fatehi, Farzad AD - Graduate University of Advanced Technology, Kerman, Iran. AD - University of Sussex, Brighton, United Kingdom. Y1 - 2017 PY - 2017 VL - 4 IS - 2 SP - 61 EP - 67 KW - projectional inequality KW - Linear preserver KW - inequality of vectors DO - 10.22072/wala.2017.63024.1115 N2 - This paper introduces an inequality on vectors in $\mathbb{R}^n$ which compares vectors in $\mathbb{R}^n$ based on the $p$-norm of their projections on $\mathbb{R}^k$ ($k\leq n$). For $p>0$, we say $x$ is $d$-projectionally less than or equal to $y$ with respect to $p$-norm if $\sum_{i=1}^k\vert x_i\vert^p$ is less than or equal to $ \sum_{i=1}^k\vert y_i\vert^p$, for every $d\leq k\leq n$. For a relation $\sim$ on a set $X$, we say a map $f:X \rightarrow X$ is a preserver of that relation, if $x\sim y$ implies $f(x)\sim f(y)$, for every $x,y\in X$. All the linear maps that preserve $d$-projectional equality and inequality are characterized in this paper. UR - https://wala.vru.ac.ir/article_29391.html L1 - https://wala.vru.ac.ir/article_29391_0c3c85a7a89bc6f8ac60bfcc89b198b0.pdf ER -