J. Ka̧kol

activity

20142022

most citedJosefson-Nissenzweig property for

C_{p}

-spaces

21 citations · 77 across the 14 of their papers we have counts for

collaborators

17 papers

math.FA2022

When is a locally convex space Eberlein-Grothendieck?

Jerzy Kakol, Arkady Leiderman

In this paper we undertake a systematic study of those locally convex spaces $E$ such that $(E, w)$ is (linearly) Eberlein-Grothendieck, where $w$ is the weak topology of $E$ . Let…

math.GN2021

On linear continuous operators between distinguished spaces $C_{p} (X)$

Jerzy Kakol, Arkady Leiderman

As proved in [16], for a Tychonoff space $X$ , a locally convex space $C_{p} (X)$ is distinguished if and only if $X$ is a $Δ$ -space. If there exists a linear continuous surjective m…

math.GN2021★ 2 cited

Basic properties of $X$ for which spaces $C_{p} (X)$ are distinguished

Jerzy Kakol, Arkady Leiderman

In our paper [18] we showed that a Tychonoff space $X$ is a $Δ$ -space (in the sense of [20], [30]) if and only if the locally convex space $C_{p} (X)$ is distinguished. Continuing t…

math.GN2020

$ω^{ω}$ -Base and infinite-dimensional compact sets in locally convex spaces

Taras Banakh, Jerzy Kąkol, Johannes Phillip Schürz

A locally convex space (lcs) $E$ is said to have an $ω^{ω}$ -base if $E$ has a neighborhood base ${U_{α} : α \in ω^{ω}}$ at zero such that $U_{β} \subseteq U_{α}$ for all $α \leq β$ . The class of…

math.GN2020★ 2 cited

On complemented copies of the space $c_{0}$ in spaces $C_{p} (X \times Y)$

Jerzy Kąkol, Witold Marciszewski, Damian Sobota +1

Cembranos and Freniche proved that for every two infinite compact Hausdorff spaces $X$ and $Y$ the Banach space $C (X \times Y)$ of continuous real-valued functions on $X \times Y$ en…

math.FA2018

Dunford--Pettis type properties and the Grothendieck property for function spaces

Saak Gabriyelyan, Jerzy Kcakol

For a Tychonoff space $X$ , let $C_{k} (X)$ and $C_{p} (X)$ be the spaces of real-valued continuous functions $C (X)$ on $X$ endowed with the compact-open topology and the pointwise topolo…

math.FA2018★ 21 cited

Josefson-Nissenzweig property for $C_{p}$ -spaces

T. Banakh, J. Kąkol, W. Śliwa

The famous Rosenthal-Lacey theorem asserts that for each infinite compact space $K$ the Banach space $C (K)$ admits a quotient which is either a copy of $c_{0}$ or $ℓ_{2}$ . The a…

math.GN2018★ 20 cited

Metrizable quotients of $C_{p}$ -spaces

T. Banakh, J. Kąkol, W. Śliwa

The famous Rosenthal-Lacey theorem asserts that for each infinite compact set $K$ the Banach space $C (K)$ admits a quotient which is either a copy of $c$ or $ℓ_{2}$ . What is the…

math.FA2017

On the separable quotient problem for Banach spaces

J. C. Ferrando, J. Kakol, M. Lopez-Pellicer +1

While the classic separable quotient problem remains open, we survey general results related to this problem and examine the existence of a particular infinitedimensional separable…

math.GN2016

The Ascoli property for function spaces

Saak Gabriyelyan, Jan Grebík, Jerzy Kakol +1

The paper deals with Ascoli spaces $C_{p} (X)$ and $C_{k} (X)$ over Tychonoff spaces $X$ . The class of Ascoli spaces $X$ , i.e. spaces $X$ for which any compact subset $K$ of $C_{k} (X)$ is…

math.GN2016

Topological properties of function spaces over ordinals

Saak Gabriyelyan, Jan Grebik, Jerzy Kakol +1

A topological space $X$ is said to be an Ascoli space if any compact subset $K$ of $C_{k} (X)$ is evenly continuous. This definition is motivated by the classical Ascoli theorem. We s…

math.FA2016

Free locally convex spaces with a small base

Saak Gabriyelyan, Jerzy Kakol

The paper studies the free locally convex space $L (X)$ over a Tychonoff space $X$ . Since for infinite $X$ the space $L (X)$ is never metrizable (even not Fréchet-Urysohn), a possibl…

math.FA2015★ 7 cited

The Ascoli property for function spaces and the weak topology of Banach and Fréchet spaces

S. Gabriyelyan, J. Kakol, G. Plebanek

Following [3] we say that a Tychonoff space $X$ is an Ascoli space if every compact subset $K$ of $C_{k} (X)$ is evenly continuous; this notion is closely related to the cla…

math.GN2015★ 4 cited

On topological properties of the weak topology of a Banach space

Saak Gabriyelyan, Jerzy Kakol, Lyubomyr Zdomskyy

Being motivated by the famous Kaplansky theorem we study various sequential properties of a Banach space $E$ and its closed unit ball $B$ , both endowed with the weak topology of $E…

math.FA2014★ 20 cited

Networks for the weak topology of Banach and Fréchet spaces

S. Gabriyelyan, J. Kcakol, W. Kubiś +1

We start the systematic study of Fréchet spaces which are $ℵ$ -spaces in the weak topology. A topological space $X$ is an $ℵ_{0}$ -space or an $ℵ$ -space if $X$ has a cou…

math.GN2014

On topological spaces and topological groups with certain local countable networks

S. S. Gabriyelyan, J. Kakol

Being motivated by the study of the space $C_{c} (X)$ of all continuous real-valued functions on a Tychonoff space $X$ with the compact-open topology, we introduced in [15] the concep…

math.GN2014★ 1 cited

On $P$ -spaces and related concepts

S. S. Gabriyelyan, J. Kakol

The concept of the strong Pytkeev property, recently introduced by Tsaban and Zdomskyy in [32], was successfully applied to the study of the space $C_{c} (X)$ of all continuous real-v…

When is a locally convex space Eberlein-Grothendieck?

On linear continuous operators between distinguished spaces Cp​(X)

Basic properties of X for which spaces Cp​(X) are distinguished

ωω-Base and infinite-dimensional compact sets in locally convex spaces

On complemented copies of the space c0​ in spaces Cp​(X×Y)

Dunford--Pettis type properties and the Grothendieck property for function spaces

Josefson-Nissenzweig property for Cp​-spaces

Metrizable quotients of Cp​-spaces

On the separable quotient problem for Banach spaces

The Ascoli property for function spaces

Topological properties of function spaces over ordinals

Free locally convex spaces with a small base

The Ascoli property for function spaces and the weak topology of Banach and Fréchet spaces

On topological properties of the weak topology of a Banach space

Networks for the weak topology of Banach and Fréchet spaces

On topological spaces and topological groups with certain local countable networks

On P-spaces and related concepts

On linear continuous operators between distinguished spaces $C_{p} (X)$

Basic properties of $X$ for which spaces $C_{p} (X)$ are distinguished

$ω^{ω}$ -Base and infinite-dimensional compact sets in locally convex spaces

On complemented copies of the space $c_{0}$ in spaces $C_{p} (X \times Y)$

Josefson-Nissenzweig property for $C_{p}$ -spaces

Metrizable quotients of $C_{p}$ -spaces

On $P$ -spaces and related concepts