Some projections and their properties in the space $l^{mn}_{\infty }$ ($m\geq 2$, $n\geq 3$)
Volume 128 / 2022
Annales Polonici Mathematici 128 (2022), 221-232
MSC: Primary 46B20; Secondary 41A52.
DOI: 10.4064/ap210405-8-3
Published online: 10 June 2022
Abstract
The paper considers projections of the space $l_\infty ^{mn}$ onto a certain class of subspaces of codimension $m$, which are formed by using hyperplanes of $l_\infty ^{mn}$. For them we find relative projection constants and constants of strong uniqueness. In some of the cases under consideration, the relative projection constant is equal to $1$, and in others it is greater than $1$. The maximum values of the constants of strong uniqueness are calculated for the projections with unit norm.
