4 citations · 9 across the 6 of their papers we have counts for
8 papers
Finite-dimensional normed spaces without small-norm hyperplane projections
Tomasz Kobos
We prove that there exists an absolute constant such that for every there exists an -dimensional real normed space for which every linear projection ont…
Spaces with the maximal projection constant revisited
Tomasz Kobos
Let be an integer such that an equiangular set of vectors of the maximal possible cardinality (that is, attaining the classical Gerzon upper bound) ex…
-strong uniqueness of a best approximation and of minimal projections in complex polytope norms and their duals
Tomasz Kobos, Grzegorz Lewicki
We study a property of -strong uniqueness of a best approximation in a class of finite-dimensional complex normed spaces, for which the unit ball is an absolutely convex hull of…
On the dimension of the set of minimal projections
Tomasz Kobos, Grzegorz Lewicki
Let be a finite-dimensional normed space and let be its proper linear subspace. The set of all minimal projections from to is a convex subset of the spa…
A uniform estimate of the relative projection constant
Tomasz Kobos
The main goal of the paper is to provide a quantitative lower bound greater than for the relative projection constant , where is a subspace of space…
Hyperplanes of finite-dimensional normed spaces with the maximal relative projection constant
Tomasz Kobos
The \emph{relative projection constant} of normed spaces is defined as , where den…
Around the Petty theorem on equilateral sets
Tomasz Kobos
The main goal of this paper is to provide an alternative proof of the following theorem of Petty: in the normed space of dimension at least three, every 3-element equilateral set c…
Equilateral dimension of some classes of normed spaces
Tomasz Kobos
An equilateral dimension of a normed space is a maximal number of pairwise equidistant points of this space. The aim of this paper is to study the equilateral dimension of certain…