modular space

Let $\rho$ be a modular on a real or complex vector space $X$. Then the subspace

$$X_{\rho }:=\{x\in X:\underset{\lambda \to 0}{lim}\rho (\lambda x)=0\}$$

of $X$ is called the modular space corresponding to the modular $\rho$.

Title	modular space
Canonical name	ModularSpace
Date of creation	2013-03-22 16:15:53
Last modified on	2013-03-22 16:15:53
Owner	gilbert_51126 (14238)
Last modified by	gilbert_51126 (14238)
Numerical id	6
Author	gilbert_51126 (14238)
Entry type	Definition
Classification	msc 46-00