Tomasz Kobos

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20172026

most citedExtremal Banach-Mazur distance between a symmetric convex body and an arbitrary convex body on the plane

3 citations · 3 across the 9 of their papers we have counts for

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math.FA2026

A Complex Analogue of Spencer's Six Standard Deviations Theorem and the Complex Banach-Mazur Distance

Tomasz Kobos, Marin Varivoda

We investigate a complex analogue of Spencer's Six Standard Deviations Theorem. Specifically, we propose the following conjecture: for any dimension $n \geq 2$ , given vectors $a_1,…

math.FA2022

On non-linear mappings preserving the semi-inner product

Tomasz Kobos, Paweł Wójcik

We say that a smooth normed space $X$ has a property (SL), if every mapping $f : X \to X$ preserving the semi-inner product on $X$ is linear. It is well known that every Hilbert spac…

math.FA2020

A uniform lower bound on the norms of hyperplane projections of spherical polytopes

Tomasz Kobos

Let $K$ be a centrally symmetric spherical and simplicial polytope, whose vertices form a $\frac{1}{4 n} -$ net in the unit sphere in $R^{n}$ . We prove a uniform lower bound on…

math.FA2017★ 3 cited

Extremal Banach-Mazur distance between a symmetric convex body and an arbitrary convex body on the plane

Tomasz Kobos

We prove that if $K, L \subset R^{2}$ are convex bodies such that $L$ is symmetric and the Banach-Mazur distance between $K$ and $L$ is equal to $2$ , then $K$ is a triangle.

math.FA2017

Stability result for the extremal Grünbaum distance between convex bodies

Tomasz Kobos

In 1963 Grünbaum introduced the following variation of the Banach-Mazur distance for arbitrary convex bodies $K, L \subset R^{n}$ : $d_G(K, L) = \inf \{ |r| \ : \ K' \subset…