Zobrazeno 1 - 10
of 19
pro vyhledávání: '"Artur Wachowicz"'
We prove that the lower density operator associated with the Baire category density points in the real line has Borel values of class $$\pmb \Pi ^0_3$$ Π 3 0 which is analogous to the measure case. We also introduce the notion of the Baire category
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d24e519d0e060519dfce95887d66c4b5
Publikováno v:
Acta Mathematica Hungarica. 150:312-323
We investigate the Baire category of \({\mathcal{I}}\)-convergent subsequences and rearrangements of a divergent sequence s = (sn) of reals if \({\mathcal{I}}\) is an ideal on \({\mathbb{N}}\) having the Baire property. We also discuss the measure of
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::8300d9eefb818dbc5f6c3a8687082b74
https://doi.org/10.1007/s10474-016-0644-8
https://doi.org/10.1007/s10474-016-0644-8
Publikováno v:
Quaestiones Mathematicae; Vol 42, No 6 (2019); 765-779
Assume that $\mathcal{I}$ is an ideal on $\mathbb{N}$, and $\sum_n x_n$ is a divergent series in a Banach space $X$. We study the Baire category, and the measure of the set $A(\mathcal{I}):=\left\{t \in \{0,1\}^{\mathbb{N}} \colon \sum_n t(n)x_n \tex
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::68777bff6f5c1e8d70bc5b2cc6514a60
http://arxiv.org/abs/1803.03699
http://arxiv.org/abs/1803.03699
Publikováno v:
Journal of Mathematical Analysis and Applications. 375:431-435
We answer the questions asked by Faisant et al. (2005) [2] . The first main result states that for every admissible ideal I ⊂ P ( N ) the quotient space l ∞ ( I ) / c 0 ( I ) is complete. The second main result states that consistently there is a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d34f22867c4a5b3ef885b31b9da2878b
https://doi.org/10.1016/j.jmaa.2010.09.023
https://doi.org/10.1016/j.jmaa.2010.09.023
Let 𝓙 be an ideal on ℕ which is analytic or coanalytic. Assume that (fn ) is a sequence of functions with the Baire property from a Polish space X into a Polish space Z, which is divergent on a comeager set. We investigate the Baire category of
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b37be8022954fce00c91e08957c86049
Autor:
Artur Wachowicz
Publikováno v:
gmj. 12:763-768
Let 𝐶 = 𝐶[0, 1] denote the Banach space of continuous real functions on [0, 1] with the sup norm and let 𝐶* denote the topological subspace of 𝐶 consisting of functions with values in [0, 1]. We investigate the preimages of residual sets
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::047a373cc10d2b628d2df5e1bd2d51ca
https://doi.org/10.1515/gmj.2005.763
https://doi.org/10.1515/gmj.2005.763
Publikováno v:
Studia Mathematica. 170:203-209
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::3b4aab122981bfd299115fa27dac5fda
https://doi.org/10.4064/sm170-2-5
https://doi.org/10.4064/sm170-2-5
Publikováno v:
Taiwanese J. Math. 17, no. 3 (2013), 1115-1126
We show that, for several function Banach spaces, multiplication considered as a bilinear continuous srjection, is an open mapping. In particular, we prove that multiplication from $L_p \times L_q$ to $L_1$ (for $p,q \in [1,\infty]$, $1/p + 1/q = 1$)
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::113a7f0d5cedea168f58d8e363fbad66
http://projecteuclid.org/euclid.twjm/1499706001
http://projecteuclid.org/euclid.twjm/1499706001
Udostępnienie publikacji Wydawnictwa Uniwersytetu Łódzkiego finansowane w ramach projektu „Doskonałość naukowa kluczem do doskonałości kształcenia”. Projekt realizowany jest ze środków Europejskiego Funduszu Społecznego w ramach Progr
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8151bc6cdc636c7efaab6bd27ef3e884
https://hdl.handle.net/11089/28703
https://hdl.handle.net/11089/28703
Autor:
Artur Wachowicz
Publikováno v:
Real Analysis Exchange. 34:445
Let $C^{(n)}[0,1]$ stand for the Banach space of functions $f:[0,1]\rightarrow \mathbb{R}$ with continuous $n$ -th derivative. We prove that if $B_{1},B_{2}$ are open balls in $C^{(n)}[0,1]$ then the set $B_{1}\cdot B_{2}=\{f\cdot g:f\in B_{1},g\in B
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::beff0152c45dc460f5a8bdac3655c772
https://doi.org/10.14321/realanalexch.34.2.0445
https://doi.org/10.14321/realanalexch.34.2.0445