What does the double asterisk mean here?

[seriously disabled]

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.

[ajb]

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

[seriously disabled]

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, 2009 by Uri

[ajb]

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.