Zobrazeno 1 - 10
of 147
pro vyhledávání: '"Plebanek, Grzegorz"'
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 complemented subspace isometric to the Banach space $C(G)$. Consequently,
Externí odkaz:
http://arxiv.org/abs/2405.19120
Autor:
Plebanek, Grzegorz
Given a compact space $K$, we denote by $P(K)$ the space of all Radon probability measures on $K$, equipped with the $weak^\ast$ topology inherited from $C(K)^\ast$. For nonmetrizable compacta $K$ even basic properties of $P(K)$ spaces depend of addi
Externí odkaz:
http://arxiv.org/abs/2312.14755
Autor:
Korpalski, Maciej, Plebanek, Grzegorz
We consider a separable compact line $K$ and its extension $L$ consisting of $K$ and a countable number of isolated points. The main object of study is the existence of a bounded extension operator $E: C(K)\to C(L)$. We show that if such an operator
Externí odkaz:
http://arxiv.org/abs/2305.04565
We prove that there is a compact space $L$ and a 1-complemented subspace of the Banach space $C(L)$ which is not isomorphic to a space of continuous functions.
Comment: Final version of May 7, 2023; 19 pages
Comment: Final version of May 7, 2023; 19 pages
Externí odkaz:
http://arxiv.org/abs/2111.13860
For any cardinal number $\kappa$ and an index set $\Gamma$, $\Sigma_\kappa$-product of real lines consists of elements of ${\mathbb R}^\Gamma$ having $<\kappa$ nonzero coordinates. A compact space $K$ is $\kappa$-Corson compact if it can be embedded
Externí odkaz:
http://arxiv.org/abs/2107.02513
It follows from a theorem of Rosenthal that a compact space is $ccc$ if and only if every Eberlein continuous image is metrizable. Motivated by this result, for a class of compact spaces $\mathcal{C}$ we define its orthogonal $\mathcal{C}^\perp$ as t
Externí odkaz:
http://arxiv.org/abs/2104.06065
Autor:
Plebanek, Grzegorz
We present a connected version of the compact $L$-space constructed by Kenneth Kunen under CH. We show that this provides a Corson compact space $K$ such that the Banach space $C(K)$ is isomorphic to no space of continuous function on a zero-dimensio
Externí odkaz:
http://arxiv.org/abs/2012.01849
Autor:
Plebanek, Grzegorz
For a compact space $K$ we consider the space $P(K)$, of probability regular Borel measures on $K$, equipped with the $weak^\ast$ topology inherited from $C(K)^\ast$. We discuss possible characterizations of those compact spaces $K$ for which $P(K)$
Externí odkaz:
http://arxiv.org/abs/1912.13297
Autor:
Sánchez, Félix Cabello, Castillo, Jesús M. F., Marciszewski, Witold, Plebanek, Grzegorz, Salguero-Alarcón, Alberto
We discuss three problems of Koszmider on the structure of the spaces of continuous functions on the Stone compact $K_{\mathcal A}$ generated by an almost disjoint family $\mathcal A$ of infinite subsets of $\omega$ -- we present a solution to two pr
Externí odkaz:
http://arxiv.org/abs/1910.07273
Publikováno v:
In Advances in Mathematics 1 August 2023 426
