Damian Sobota

activity

20142026

most citedConvergence of measures in forcing extensions

17 citations · 23 across the 19 of their papers we have counts for

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14 papers · 1 filter

math.FA2026

A small Banach space $C (K)$ without nice renormings

Todor Manev, Damian Sobota, Lyubomyr Zdomskyy

We prove that consistently $ω_{1} < c$ and there exists a compact space $K$ whose Banach space $C (K)$ of continuous real-valued functions is Grothendieck, has density $ω_{1}$ ,…

math.FA2026

Complementability of separable spaces $C (K)$ in Banach spaces

Jakub Rondoš, Damian Sobota

For a metric compact space $L$ and a Banach space $E$ , we provide a characterization of the complementability of the Banach space $C (L)$ of continuous functions on $L$ in…

math.FA2025

A small remark on small-dimensional normed barrelled spaces

Damian Sobota

Combining the methods of Brian and Stuart with the classical Dvoretzky theorem, we show that no infinite-dimensional Banach space contains a barrelled subspace of (algebraic) dimen…

math.FA2024

Complemented subspaces of Banach spaces $C (K \times L)$

Grzegorz Plebanek, Jakub Rondoš, Damian Sobota

We prove that, for every compact spaces $K_{1}, K_{2}$ and compact group $G$ , if both $K_{1}$ and $K_{2}$ map continuously onto $G$ , then the Banach space $C (K_{1} \times K_{2})$ contains a com…

math.FA2024

Continuous operators from spaces of Lipschitz functions

Christian Bargetz, Jerzy Kąkol, Damian Sobota

We study the existence of continuous (linear) operators from the Banach spaces $\mbox{Lip}_0(M)$ of Lipschitz functions on infinite metric spaces $M$ vanishing at a distinguished p…

math.FA2023

Construction under Martin's axiom of a Boolean algebra with the Grothendieck property but without the Nikodym property

Damian Sobota, Lyubomyr Zdomskyy

Improving a result of M. Talagrand, under the assumption of a weak form of Martin's axiom, we construct a totally disconnected compact Hausdorff space $K$ such that the Banach spac…

math.FA2022

On complementability of $c_{0}$ in spaces $C (K \times L)$

Jerzy Kąkol, Damian Sobota, Lyubomyr Zdomskyy

Using elementary probabilistic methods, in particular a variant of the Weak Law of Large Numbers related to the Bernoulli distribution, we prove that for every infinite compact spa…

math.FA2022

Grothendieck $C (K)$ -spaces and the Josefson--Nissenzweig theorem

Jerzy Kąkol, Damian Sobota, Lyubomyr Zdomskyy

For a compact space $K$ , the Banach space $C (K)$ is said to have the $ℓ_{1}$ -Grothendieck property if every weak* convergent sequence $⟨ μ_{n} : n \in ω ⟩$ of f…

math.FA2022

The Josefson--Nissenzweig theorem and filters on $ω$

Witold Marciszewski, Damian Sobota

For a free filter $F$ on $ω$ , endow the space $N_{F} = ω \cup {p_{F}}$ , where $p_{F} \neq \in ω$ , with the topology in which every element of $ω$ is isolated whereas all open neighborhoods of…

math.FA2021

On complemented copies of the space $c_{0}$ in spaces $C_{p} (X, E)$

Christian Bargetz, Jerzy Kąkol, Damian Sobota

We study the question for which Tychonoff spaces $X$ and locally convex spaces $E$ the space $C_{p} (X, E)$ of continuous $E$ -valued functions on $X$ contains a complemented copy of th…

math.FA2021

Minimally generated Boolean algebras and the Nikodym property

Damian Sobota, Lyubomyr Zdomskyy

A Boolean algebra $A$ has the Nikodym property if every pointwise bounded sequence of bounded finitely additive measures on $A$ is uniformly bounded. Assuming the…

math.FA2020★ 4 cited

The Josefson--Nissenzweig theorem, Grothendieck property, and finitely supported measures on compact spaces

Jerzy Kąkol, Damian Sobota, Lyubomyr Zdomskyy

The celebrated Josefson-Nissenzweig theorem implies that for a Banach space $C (K)$ of continuous real-valued functions on an infinite compact space $K$ there exists a sequence of R…

math.FA2019★ 17 cited

Convergence of measures in forcing extensions

Damian Sobota, Lyubomyr Zdomskyy

We prove that if $A$ is a $σ$ -complete Boolean algebra in a model $V$ of set theory and $P \in V$ is a proper forcing with the Laver property preserving the groun…

math.FA2014

Countable tightness in the spaces of regular probability measures

Grzegorz Plebanek, Damian Sobota

We prove that if $K$ is a compact space and the space $P (K \times K)$ of regular probability measures on $K \times K$ has countable tightness in its $w e a k^{*}$ topology, then $L_{1} (μ)$ …

A small Banach space C(K) without nice renormings

Complementability of separable spaces C(K) in Banach spaces

A small remark on small-dimensional normed barrelled spaces

Complemented subspaces of Banach spaces C(K×L)

Continuous operators from spaces of Lipschitz functions

Construction under Martin's axiom of a Boolean algebra with the Grothendieck property but without the Nikodym property

On complementability of c0​ in spaces C(K×L)

Grothendieck C(K)-spaces and the Josefson--Nissenzweig theorem

The Josefson--Nissenzweig theorem and filters on ω

On complemented copies of the space c0​ in spaces Cp​(X,E)

Minimally generated Boolean algebras and the Nikodym property

The Josefson--Nissenzweig theorem, Grothendieck property, and finitely supported measures on compact spaces

Convergence of measures in forcing extensions

Countable tightness in the spaces of regular probability measures

A small Banach space $C (K)$ without nice renormings

Complementability of separable spaces $C (K)$ in Banach spaces

Complemented subspaces of Banach spaces $C (K \times L)$

On complementability of $c_{0}$ in spaces $C (K \times L)$

Grothendieck $C (K)$ -spaces and the Josefson--Nissenzweig theorem

The Josefson--Nissenzweig theorem and filters on $ω$

On complemented copies of the space $c_{0}$ in spaces $C_{p} (X, E)$