Tomasz Kania

collaborators

5 papers

math.FA2026

$(λ^{+})$ -injective Banach spaces

Tomasz Kania, Grzegorz Lewicki

In a companion paper (Studia Math., 2023), we proved for every $λ \in (1, 2]$ the existence of a $(λ^{+})$ -injective renorming of $ℓ_{\infty}$ that is not $λ$ -injective, thereby establ…

q-fin.RM2026

Coherent risk from finite models

Tomasz Kania

Coherent estimators at different sample sizes need not describe the same population risk. We prove that dyadic estimators do so exactly when duplicating every scenario leaves the e…

math.FA2025

Raja's covering index of $L_{p}$ spaces

Tomasz Kania, Natalia Maślany

We study Raja's covering index $Θ_{X} (n)$ for classical $L_{p}$ -spaces and their non-commutative counterparts. For infinite-dimensional Hilbert spaces we compute the covering index exa…

math.CA2025

Parallelepipeds of maximal facet area and total edge length in ellipsoids, through prescribed boundary points

Tomasz Kania

Let \[ \mathcal{E}_A=\{x\in\mathbb{R}^n:x^{\top}A^{-1}x\le 1\},\qquad n\ge2, \] where $A$ is real symmetric positive definite. We study full-dimensional parallelepipeds whose $2^{n}$ …

math.SP2025

Dimension-dependent bounds for the SDIEP via phase optimisation and Paley-type constructions

Tomasz Kania

We refine the cycle-walk (Fourier) template of Gnacik and the author to quantify when a~ $δ$ -Sule\uımanova spectrum $(1, λ_{2}, \dots, λ_{n})$ (with $λ_{j} \leq 0$ ) is realised by a symmetric…

(λ+)-injective Banach spaces

Coherent risk from finite models

Raja's covering index of Lp​ spaces

Parallelepipeds of maximal facet area and total edge length in ellipsoids, through prescribed boundary points

Dimension-dependent bounds for the SDIEP via phase optimisation and Paley-type constructions

$(λ^{+})$ -injective Banach spaces

Raja's covering index of $L_{p}$ spaces