modular mappings in vector spaces over the field of complex numbers
Suppose $X$ is a $\u2102$vector space. A mapping $\rho :X\to [0,\mathrm{\infty}]$ is called modular if the following three conditions are satisfied:

1.
$\rho (x)=0$ if and only if $x=0$.

2.
$\rho (\alpha x)=\rho (x)$ for all $x\in X$ and for all scalars $\alpha $ such that $\alpha =1$.

3.
$\rho (\alpha x+\beta y)\le \rho (x)+\rho (y)$ for all $x,y\in X$ and for all scalars $\alpha $ and $\beta $ such that $\alpha +\beta =1$ and $\alpha ,\beta \ge 0$.
Title  modular mappings in vector spaces over the field of complex numbers^{} 

Canonical name  ModularMappingsInVectorSpacesOverTheFieldOfComplexNumbers 
Date of creation  20130322 16:08:12 
Last modified on  20130322 16:08:12 
Owner  gilbert_51126 (14238) 
Last modified by  gilbert_51126 (14238) 
Numerical id  11 
Author  gilbert_51126 (14238) 
Entry type  Definition 
Classification  msc 4600 
Defines  modular 