Description

• Title:
  Function bases for topological vector spaces
• Creator:
  Yilmaz, Yilmaz
• Description:
  Our main interest in this work is to characterize certain operator spaces acting on some important vector-valued function spaces such as $(V_{a}) _{c_{0}}^{a\in{\mathbb A}}$, by introducing a new kind basis notion for general Topological vector spaces. Where ${\mathbb A}$ is an infinite set, each $V_{a}$ is a Banach space and $( V_{a}) _{c_{0}}^{a\in{\mathbb A}}$ is the linear space of all functions $x\colon{\mathbb A} \rightarrow\bigcup V_{a}$ such that, for each $\varepsilon> 0$, the set $\{ a\in{\mathbb A}:\Vert x_{a}\Vert > \varepsilon\} $ is finite or empty. This is especially important for the vector-valued sequence spaces $( V_{i}) _{c_{0}}^{i\in{\mathbb N}}$ because of its fundamental place in the theory of the operator spaces (see, for example,[H. P. Rosenthal, {\it The complete separable extension property}, J. Oper. Theory, 43, No. 2, (2000), 329-374]).
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2009.06.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 33, No 2 (June 2009); 335 - 353;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2009.023/8631
• Subject:
  Biorthogonal systems;
  Schauder bases;
  generalization of bases;
  operators on function spaces;
  vector-valued function spaces;
  representation of operators;
  Primary 46A35;
  46B15;
  47B38;
  Secondary 46B28;
  46B45;
  46E28;
  42C05
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2009.023
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other