Temat: normed space - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Some Ramsey type theorems for normed and quasinormed spaces
Autorzy:: Henson, C. Ward
Kalton, Nigel
Peck, N.
Tereščák, Ignác
Zlatoš, Pavol
Powiązania:: https://bibliotekanauki.pl/articles/1219937.pdf
Data publikacji:: 1997
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: normed space
Banach space
quasinormed and quasi-Banach space
p-norm
biorthogonal sequence
uniformly independent sequence
irreducible sequence
Ramsey's Theorem
nonstandard analysis
Opis:: We prove that every bounded, uniformly separated sequence in a normed space contains a "uniformly independent" subsequence (see definition); the constants involved do not depend on the sequence or the space. The finite version of this result is true for all quasinormed spaces. We give a counterexample to the infinite version in $L_p[0,1]$ for each 0 < p < 1. Some consequences for nonstandard topological vector spaces are derived.
Źródło:: Studia Mathematica; 1997, 124, 1; 81-100
0039-3223
Pojawia się w:: Studia Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: Rotundity and smoothness of convex bodies in reflexive and nonreflexive spaces
Autorzy:: Klee, Victor
Veselý, Libor
Zanco, Clemente
Powiązania:: https://bibliotekanauki.pl/articles/1287312.pdf
Data publikacji:: 1996
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: normed linear space
reflexive
convex body
smooth
rotund
strictly convex
vector sum
convex hull
stability
Opis:: For combining two convex bodies C and D to produce a third body, two of the most important ways are the operation ∓ of forming the closure of the vector sum C+D and the operation γ̅ of forming the closure of the convex hull of C ⋃ D. When the containing normed linear space X is reflexive, it follows from weak compactness that the vector sum and the convex hull are already closed, and from this it follows that the class of all rotund bodies in X is stable with respect to the operation ∓ and the class of all smooth bodies in X is stable with respect to both ∓ and γ̅. In our paper it is shown that when X is separable, these stability properties of rotundity (resp. smoothness) are actually equivalent to the reflexivity of X. The characterizations remain valid for each nonseparable X that contains a rotund (resp. smooth) body.
Źródło:: Studia Mathematica; 1996, 120, 3; 191-204
0039-3223
Pojawia się w:: Studia Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

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