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1
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Boundaries of upper semicontinuous set valued maps

100%
Labuda I.
Commentationes Mathematicae
|
2005
|
tom 45
|
nr 2
EN
Let \(x_0\) be a q-point of a regular space \(X, Y\) a Hausdorff space whose relatively countably compact subsets are relatively compact and let \(F\colon X \to Y\) be an upper semicontinuous set valued map. Then the active boundary \(\operatorname{Frac} F (x_0)\) is the smallest compact kernel of \(F\) at \(x_0\).
2
Content available remote

Alexander Subbase Theorem for Filters

100%
Labuda I.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2006
|
tom 54
|
nr 2
147-152
EN
The theorem in the title is proven. Applications to product theorems are given.
3
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Domains of integral operators

64%
Labuda I., Szeptycki P.
Studia Mathematica
|
1994
|
tom 111
|
nr 1
53-68
EN
It is shown that the proper domains of integral operators have separating duals but in general they are not locally convex. Banach function spaces which can occur as proper domains are characterized. Some known and some new results are given, illustrating the usefulness of the notion of proper domain.
4
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Vector series whose lacunary subseries converge

64%
Drewnowski L., Labuda I.
Studia Mathematica
|
2000
|
tom 138
|
nr 1
53-80
EN
The area of research of this paper goes back to a 1930 result of H. Auerbach showing that a scalar series is (absolutely) convergent if all its zero-density subseries converge. A series $∑_n x_n$ in a topological vector space X is called ℒ-convergent if each of its lacunary subseries $∑_k x_{n_k}$ (i.e. those with $n_{k+1} - n_k → ∞$) converges. The space X is said to have the Lacunary Convergence Property, or LCP, if every ℒ-convergent series in X is convergent; in fact, it is then subseries convergent. The Zero-Density Convergence Property, or ZCP, is defined similarly though of lesser importance here. It is shown that for every ℒ-convergent series the set of all its finite sums is metrically bounded; however, it need not be topologically bounded. Next, a space with the LCP contains no copy of the space $c_0$. The converse holds for Banach spaces and, more generally, sequentially complete locally pseudoconvex spaces. However, an F-lattice of measurable functions is constructed that has both the Lebesgue and Levi properties, and thus contains no copy of $c_0$, and, nonetheless, lacks the LCP. The main (and most difficult) result of the paper is that if a Banach space E contains no copy of $c_0$ and λ is a finite measure, then the Bochner space $L_0$ (λ,e) has the LCP. From this, with the help of some Orlicz-Pettis type theorems proved earlier by the authors, the LCP is deduced for a vast class of spaces of (scalar and vector) measurable functions that have the Lebesgue type property and are "metrically-boundedly sequentially closed" in the containing $L_0$ space. Analogous results about the convergence of ℒ-convergent positive series in topological Riesz spaces are also obtained. Finally, while the LCP implies the ZCP trivially, an example is given that the converse is false, in general.
5
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Problem 24 of the "Scottish book'' concerning additive functionals

45%
Labuda I., Mauldin R. D.
Colloquium Mathematicum
|
1984
|
tom 48
|
nr 1
89-91
6
Content available remote

Completeness type properties of locally solid Riesz spaces

32%
Labuda I.
Studia Mathematica
|
1983-1984
|
tom 77
|
nr 4
349-372
7
Content available remote

Exhaustive measures in arbitrary topological vector spaces

32%
Labuda I.
Studia Mathematica
|
1976
|
tom 58
|
nr 3
239-248
8
Content available remote

On boundedly order-complete locally solid Riesz spaces

32%
Labuda I.
Studia Mathematica
|
1985
|
tom 81
|
nr 3
245-258
9
Content available remote

Continuity of operators on Saks spaces

26%
Labuda I.
Studia Mathematica
|
1974
|
tom 51
|
nr 1
11-21
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