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Weight generalization of the space of continuous functions vanishing at infinity.
- Source :
-
Mathematische Nachrichten . Aug2023, Vol. 296 Issue 8, p3619-3629. 11p. - Publication Year :
- 2023
-
Abstract
- In this paper, we characterize the weighted generalization of the space of continuous functions vanishing at infinity and correct some wrong results in the paper. Let X be a locally compact space and ν is an arbitrary weight (non‐negative function) on X. We give a correct and comprehensive definition of the weighted generalization C0ν(X)$C_0^\nu (X)$ of C0(X)$C_0(X)$, and show that it is a seminormed space with respect to the canonical seminorm ∥f∥ν=supx∈X|f(x)|$\Vert f\Vert _\nu =\sup _{x\in X}|f(x)|$, where f∈C0ν(X)$f\in C_0^\nu (X)$. We find conditions on ν under which C0ν(X)$C_0^\nu (X)$, with respect to ∥.∥ν$\Vert.\Vert _\nu$, becomes a normed space or a Banach space or an algebra, or a topological algebra, respectively. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0025584X
- Volume :
- 296
- Issue :
- 8
- Database :
- Academic Search Index
- Journal :
- Mathematische Nachrichten
- Publication Type :
- Academic Journal
- Accession number :
- 169873746
- Full Text :
- https://doi.org/10.1002/mana.202200021