Temat: vector space - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: On the boundedness of sets in Musielak-Orlicz spaces
Autorzy:: Shragin, Isaac V.
Powiązania:: https://bibliotekanauki.pl/articles/745827.pdf
Data publikacji:: 2013
Wydawca:: Polskie Towarzystwo Matematyczne
Tematy:: bounded set in topological vector space, F-norm, gen-~function, Musielak-Orlicz space, right space
Opis:: The notions of metrical and topological vector boundedness of sets are considered in Musielak-Orlicz spaces. The space is called right if both these notions are equivalent. Necessary conditions of the rightness are established, and certain sufficient conditions are found.
Źródło:: Commentationes Mathematicae; 2013, 53, 2
0373-8299
Pojawia się w:: Commentationes Mathematicae
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: Arrangements of series preserving their convergence or boundedness
Autorzy:: Drewnowski, Lech
Powiązania:: https://bibliotekanauki.pl/articles/745881.pdf
Data publikacji:: 2007
Wydawca:: Polskie Towarzystwo Matematyczne
Tematy:: Convergent series
bounded series
permutations of series
arrangements of series
topological vector space
spaces of bounded or convergent series
Opis:: For a map \(\rho\) of \(\mathbb{N}\) into itself, consider the induced transformation \(\sum_{n} x_n \mapsto \sum_{n} x_{\rho_(n)}\) of series in a topological vector space. Then such properties of this transformation as sending convergent series to convergent series, or convergent series to bounded series, or bounded series to bounded series (and a few more) are mutually equivalent. Moreover, they are equivalent to an intrinsic property of ρ which reduces to those found by Agnew and Pleasants (in the case of permutations) and Wituła (in the general case) as necessary and sufficient conditions for the above transformation to preserve convergence of scalar series. In the paper, the scalar case is treated first using simple Banach space methods, and then the result is easily extended to the general setting.
Źródło:: Commentationes Mathematicae; 2007, 47, 1
0373-8299
Pojawia się w:: Commentationes Mathematicae
Dostawca treści:: Biblioteka Nauki

Artykuł

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