The continuity of superposition operators on some sequence spaces defined by moduli

Title:

The continuity of superposition operators on some sequence spaces defined by moduli

Creator:

Kolk, Enno and Raidjõe, Annemai

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:dbd27d2e-8414-4d72-a9ff-dbb50fb64f2f
uuid:dbd27d2e-8414-4d72-a9ff-dbb50fb64f2f

Subject:

sequence space, superposition operator, modulus function, and continuity

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

Let $\lambda $ and $\mu $ be solid sequence spaces. For a sequence of modulus functions $\Phi =(\varphi _{k})$ let $ \lambda (\Phi )= \lbrace x=(x_{k}) \: (\varphi _{k}(|x_{k}|))\in \lambda \rbrace $. Given another sequence of modulus functions $\Psi =(\psi _{k})$, we characterize the continuity of the superposition operators ${P_{f}}$ from $\lambda (\Phi )$ into $\mu (\Psi )$ for some Banach sequence spaces $\lambda $ and $\mu $ under the assumptions that the moduli $\varphi _{k}$ $(k \in \mathbb{N})$ are unbounded and the topologies on the sequence spaces $\lambda (\Phi )$ and $\mu (\Psi )$ are given by certain F-norms. As applications we consider superposition operators on some multiplier sequence spaces of Maddox type.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

777-792

Source:

Czechoslovak Mathematical Journal | 2007 Volume:57 | Number:3

Harvested from:

CDK

Metadata only:

false