What does the double asterisk mean here and what does [math]j_p[/math] mean ?

 

[math]j_p : L^p(\mu) \overset{\kappa_q}{\to} L^q(\mu)^* \overset{\,\,(\kappa_p^{-1})^*}{\longrightarrow} L^p(\mu)^{**}[/math]

 

This is taken from here.

The asterisk refers to the dual space. Double asterisk is the dual of the dual space, which can be identified with the original space.

But what does it mean the dual of a dual vector space? And what does the [math]j_p[/math] mean here?

Edited October 21, 200916 yr by Uri

The dual of a vector space is a vector space and so has its own dual. This is the double dual.

 

You will need to read the article carefully to figure out exactly what [math]j_{p}[/math] is. I only have a very basic knowledge of functional analysis.