18 citations · 135 across the 55 of their papers we have counts for
72 papers
Not too many miles from to
Tomasz Kania
For either real or complex scalars, we improve the known upper bound for the Banach--Mazur distance between and , proving $d_{\operatorname{BM}}(L_\inf…
Three local -characters
Tomasz Kania
We answer in ZFC a question of N. Carlson by constructing a zero-dimensional Tychonoff space , with exactly one non-isolated point, for which every point admits a decreasing loc…
Refined Gauss--Lobatto bounds for odd-order convexity
Tomasz Kania, Szymon Wąsowicz
For functions that are convex of higher order, classical extremalities identify Gaussian quadrature as a lower bound and Gauss--Lobatto quadrature as an upper bound for the integra…
Separable quotients of pointwise function spaces and relative consistency
Tomasz Kania, Jerzy Kąkol
Assuming Jensen's diamond principle, we construct a separable crowded compact zero-dimensional space of weight and cardinality such that has…
Weakly LUR norms and the Schur property
Szymon Draga, Tomasz Kania
A separable real or complex Banach space fails the Schur property if and only if it admits an equivalent Gâteaux smooth, weakly locally uniformly rotund norm which is not midpoint…
Twisting exponential spectra
Bence Horváth, Tomasz Kania
Klaja and Ransford exhibited a complex unital Banach algebra in which the exponential spectra of \(ab\) and \(ba\) differ away from zero, and asked whether this can occur in an alg…
Grothendieck and -Grothendieck subspaces of
Manuel González, Tomasz Kania
Let . We prove that contains pairwise non-isomorphic non-reflexive Grothendieck subspaces. They may all be chosen to con…
Maximal right ideals of the Banach algebra of bounded operators on a Banach space
Tomasz Kania, Niels Jakob Laustsen
We study finitely generated maximal right ideals of the Banach algebra of bounded operators on a complex Banach space . Every maximal right ideal is either fixe…
Banach's Isometric Conjecture over the Complex Field
Antonio Acuaviva, Tomasz Kania
We complete Banach's isometric conjecture over the complex field. More precisely, if \(X\) is a complex normed space and, for some \(2\leqslant n<\dim_{\C}X\), all its \(n\)-dimens…
Pointwise function spaces over compacta are not weak Banach spaces
Tomasz Kania, Jerzy Kąkol
Let be a compact Hausdorff space and let be an infinite-dimensional real Banach space. We prove that there is no continuous bijection whose inverse…
Approximate homomorphisms on orthomodular lattices
Tomasz Kania
The stability programme initiated by Ulam asks when approximate solutions to algebraic identities must lie near exact ones. For lattices, this leads to the question of when a map t…
Characterising projective and weakly projective Boolean algebras by coherent Freese--Nation separations
Tomasz Kania, Andrzej Kucharski, Sławomir Turek
We isolate a coherent finite-separation strengthening of the Freese--Nation property and use it to characterise projective and weakly projective Boolean algebras. A Boolean algebra…
Canonical reconstruction and forcing absoluteness of standard structures
Tomasz Kania
We isolate a simple preservation principle governing when it is absolute, between transitive models of set theory, that a given algebraic or topological-algebraic structure has a s…
Talagrand compacta, 2DCP, and pointwise quotients
Tomasz Kania, Jerzy Kąkol
We revisit Talagrand's CH compactum as a test object for the two-disjoint-copies property and for pointwise quotient questions. The two-disjoint-copies property, or 2DCP, is a topo…
Pure infiniteness and primary factorisation
Antonio Acuaviva, Bence Horváth, Tomasz Kania
We show that there is no real or complex indecomposable Banach space with the primary factorisation property (PFP). We relate the PFP of a Banach space to ring-theoretic infini…
Halving the original Kalton--Roberts upper bound for nearly additive set functions
Boon Suan Ho, Tomasz Kania
Let be the least constant governing uniform approximation of approximately additive real-valued set functions by finitely additive signed measures. We prove that $$K_{KR}\…
Primariness and the Primary Factorisation Property
Antonio Acuaviva, Tomasz Kania
We study the relation between primariness of Banach spaces and the stronger operator-theoretic notions of the primary factorisation property (PFP) and the uniform primary factorisa…
Quotient codings and the descriptive complexity of algebraic and analytic structures
Tomasz Kania
We study the descriptive complexity of algebraic and analytic properties by presenting structures as quotients of fixed generators. For separable Banach-type structures, admissible…
Uniform Property (S)
William B. Johnson, Tomasz Kania
We introduce and investigate a quantitative version of Steinhaus' property for Banach spaces, called the \emph{uniform property}. A Banach space is said to have unifor…
Amenability constants for unconditional sums of Banach algebras
Tomasz Kania, Jerzy Kąkol
We study Johnson amenability for unconditional direct sums of Banach algebras. Given a family of Banach algebras and a Banach sequence lattice on~, the -…
There is no universal separable Banach algebra
Tomasz Kania
We prove that no separable Banach algebra is universal for homomorphic embeddings of all separable Banach algebras, whether embeddings are merely bounded or required to be contract…
Hamana's injective envelope as a maximal rigid multiplier cover
Tomasz Kania
Let be a unital -algebra. We call an -multiplier cover a pair consisting of a -algebra and a faithful non-degenerate -homomorphism $ι\colon A\to M(E…
Law equivalence for Ornstein--Uhlenbeck dynamics driven by Lévy noise
Tomasz Kania
For stochastic partial differential equations driven by Lévy noise, understanding when changes in the drift operator preserve the law of the solution is fundamental to filtering, c…
Higher traces as boundary averages on finite-dimensional normed spaces
Tomasz Kania
Let be an -dimensional real normed space, let , and set and . We characterise the probability measures on the unit sphere…