Tomasz Kobos

activity

20132026

most citedAround the Petty theorem on equilateral sets

4 citations · 9 across the 6 of their papers we have counts for

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6 papers · 1 filter

math.FA2026

Finite-dimensional normed spaces without small-norm hyperplane projections

Tomasz Kobos

We prove that there exists an absolute constant $c > 1$ such that for every $n \geq 3$ there exists an $n$ -dimensional real normed space $X$ for which every linear projection $P$ ont…

math.FA2025

Spaces with the maximal projection constant revisited

Tomasz Kobos

Let $n \geq 2$ be an integer such that an equiangular set of vectors $w_{1}, \dots, w_{d}$ of the maximal possible cardinality (that is, attaining the classical Gerzon upper bound) ex…

math.FA2025

$2$ -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 $2$ -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…

math.FA2022

On the dimension of the set of minimal projections

Tomasz Kobos, Grzegorz Lewicki

Let $X$ be a finite-dimensional normed space and let $Y \subseteq X$ be its proper linear subspace. The set of all minimal projections from $X$ to $Y$ is a convex subset of the spa…

math.FA2015

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 $1$ for the relative projection constant $λ (Y, X)$ , where $X$ is a subspace of $ℓ_{2 p}^{m}$ space…

math.FA2014★ 2 cited

Hyperplanes of finite-dimensional normed spaces with the maximal relative projection constant

Tomasz Kobos

The \emph{relative projection constant} $λ (Y, X)$ of normed spaces $Y \subset X$ is defined as $λ (Y, X) = in f {∣∣ P ∣∣ : P \in P (X, Y)}$ , where $P (X, Y)$ den…

Finite-dimensional normed spaces without small-norm hyperplane projections

Spaces with the maximal projection constant revisited

2-strong uniqueness of a best approximation and of minimal projections in complex polytope norms and their duals

On the dimension of the set of minimal projections

A uniform estimate of the relative projection constant

Hyperplanes of finite-dimensional normed spaces with the maximal relative projection constant

$2$ -strong uniqueness of a best approximation and of minimal projections in complex polytope norms and their duals