AMUR Collection: Artykuły naukowe pracowników naukowych Wydziału Matematyki i Informatyki
https://hdl.handle.net/10593/71
Artykuły naukowe pracowników naukowych Wydziału Matematyki i Informatyki2021-01-18T15:07:01ZDescriptive Topology in non-Archimedean Function Spaces Cp(X, K). Part I
https://hdl.handle.net/10593/4327
Title: Descriptive Topology in non-Archimedean Function Spaces Cp(X, K). Part I
Authors: Śliwa, Wiesław; Kąkol, Jerzy
Abstract: Let $K$ be a non-archimedean field and let $X$ be an ultraregular space. We
study the non-archimedean locally convex space $C_p(X;K)$ of all $K$-valued continuous
functions on $X$ endowed with the pointwise topology. We show that $K$ is spherically
complete if and only if every polar metrizable locally convex space $E$ over $K$ is weakly
angelic. This extends a result of Kiyosawa - Schikhof for polar Banach spaces. For any
compact ultraregular space $X$ we prove that $C_p(X;K)$ is Frechet-Urysohn if and only if
$X$ is scattered (a non-archimedean variant of Gerlits - Pytkeev's result). If $K$ is locally
compact we show the following: (1) For any ultraregular space $X$ the space $C_p(X;K)$
is K-analytic if and only if it has a compact resolution (a non-archimedean variant of
Tkachuk's theorem); (2) For any ultrametrizable space $X$ the space $C_p(X;K)$ is analytic
if and only if $X$ is $\sigma$-compact (a non-archimedean variant of Christensen's theorem).2012-01-01T00:00:00ZOn linear isometries on non-archimedean powerseries spaces
https://hdl.handle.net/10593/4324
Title: On linear isometries on non-archimedean powerseries spaces
Authors: Śliwa, Wiesław; Ziemkowska, Agnieszka
Abstract: The non-archimedean power series spaces Ap(a; t) are the most
known and important examples of non-archimedean nuclear Frechet spaces. We
study when the spaces Ap(a; t) and Aq(b; s) are isometrically isomorphic. Next we
determine all linear isometries on the space Ap(a; t) and show that all these maps
are surjective.2012-05-01T00:00:00ZFrechet spaces of non-archimedean valued continuous functions
https://hdl.handle.net/10593/4298
Title: Frechet spaces of non-archimedean valued continuous functions
Authors: Śliwa, Wiesław
Abstract: Let $X$ be an ultraregular space and let $K$ be a complete non-archimedean
non-trivially valued field. Assume that the locally convex space $E$ = $C_c(X;K)$
of all continuous functions from $X$ to $K$ with the topology of uniform
convergence on compact subsets of $X$ is a Frechet space. We shall prove that
$E$ has an orthogonal basis consisting of $K$-valued characteristic functions of
clopen (i.e. closed and open) subsets of $X$ and that it is isomorphic to the
product of a countable family of Banach spaces with an orthonormal basis.2012-01-01T00:00:00ZThe separable quotient problem and the strongly normal sequences
https://hdl.handle.net/10593/4297
Title: The separable quotient problem and the strongly normal sequences
Authors: Śliwa, Wiesław
Abstract: We study the notion of a strongly normal sequence in the dual $E^*$ of
a Banach space $E$. In particular, we prove that the following three conditions are
equivalent:
(1) $E$ has a strongly normal sequence,
(2) $(E^*;\sigma (E ^*;E))$ has a Schauder basic sequence,
(3) $E$ has an infinite-dimensional separable quotient.2012-01-01T00:00:00Z