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1
Content available remote

Stability aspects of arithmetic functions, II

100%
Kochanek T.
Acta Arithmetica
|
2009
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tom 139
|
nr 2
131-146
2
Content available remote

Corrigendum to "Stability aspects of arithmetic functions, II" (Acta Arith. 139 (2009), 131-146)

100%
Kochanek T.
Acta Arithmetica
|
2011
|
tom 149
|
nr 1
83-98
3
Content available remote

ℱ-bases with brackets and with individual brackets in Banach spaces

100%
Kochanek T.
Studia Mathematica
|
2012
|
tom 211
|
nr 3
259-268
EN
We provide a partial answer to the question of Vladimir Kadets whether given an ℱ-basis of a Banach space X, with respect to some filter ℱ ⊂ 𝒫(ℕ), the coordinate functionals are continuous. The answer is positive if the character of ℱ is less than 𝔭. In this case every ℱ-basis is an M-basis with brackets which are determined by an element of ℱ.
4
Content available remote

Stability aspects of arithmetic functions

88%
Kochanek T.
Acta Arithmetica
|
2008
|
tom 132
|
nr 1
87-98
5
Content available remote

Probability distribution solutions of a general linear equation of infinite order, II

64%
Kochanek T., Morawiec J.
Annales Polonici Mathematici
|
2010
|
tom 99
|
nr 3
215-224
EN
Let (Ω,𝓐,P) be a probability space and let τ: ℝ × Ω → ℝ be a mapping strictly increasing and continuous with respect to the first variable, and 𝓐-measurable with respect to the second variable. We discuss the problem of existence of probability distribution solutions of the general linear equation $F(x) = ∫_Ω F(τ(x,ω)) P(dω)$. We extend our uniqueness-type theorems obtained in Ann. Polon. Math. 95 (2009), 103-114.
6
Content available remote

An inconsistency equation involving means

64%
Ger R., Kochanek T.
Colloquium Mathematicum
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2009
|
tom 115
|
nr 1
87-99
EN
We show that any quasi-arithmetic mean $A_{φ}$ and any non-quasi-arithmetic mean M (reasonably regular) are inconsistent in the sense that the only solutions f of both equations $f(M(x,y)) = A_{φ}(f(x),f(y))$ and $f(A_{φ}(x,y)) = M(f(x),f(y))$ are the constant ones.
7
Content available remote

Probability distribution solutions of a general linear equation of infinite order

64%
Kochanek T., Morawiec J.
Annales Polonici Mathematici
|
2009
|
tom 95
|
nr 2
103-114
EN
Let (Ω,𝓐,P) be a probability space and let τ: ℝ × Ω → ℝ be strictly increasing and continuous with respect to the first variable, and 𝓐-measurable with respect to the second variable. We obtain a partial characterization and a uniqueness-type result for solutions of the general linear equation $F(x) = ∫_{Ω} F(τ(x,ω))P(dω)$ in the class of probability distribution functions.
8
Content available remote

Uncountable sets of unit vectors that are separated by more than 1

64%
Kania T., Kochanek T.
Studia Mathematica
|
2016
|
tom 232
|
nr 1
19-44
EN
Let X be a Banach space. We study the circumstances under which there exists an uncountable set 𝓐 ⊂ X of unit vectors such that ||x-y|| > 1 for any distinct x,y ∈ 𝓐. We prove that such a set exists if X is quasi-reflexive and non-separable; if X is additionally super-reflexive then one can have ||x-y|| ≥ slant 1 + ε for some ε > 0 that depends only on X. If K is a non-metrisable compact, Hausdorff space, then the unit sphere of X = C(K) also contains such a subset; if moreover K is perfectly normal, then one can find such a set with cardinality equal to the density of X; this solves a problem left open by S. K. Mercourakis and G. Vassiliadis (2015).
9
Content available remote

Maximal left ideals of the Banach algebra of bounded operators on a Banach space

45%
Dales H., Kania T., Kochanek T., Koszmider P., Laustsen N.
Studia Mathematica
|
2013
|
tom 218
|
nr 3
245-286
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