seriously disabled Posted October 21, 2009 Share Posted October 21, 2009 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. Link to comment Share on other sites More sharing options...
ajb Posted October 21, 2009 Share Posted October 21, 2009 The asterisk refers to the dual space. Double asterisk is the dual of the dual space, which can be identified with the original space. Link to comment Share on other sites More sharing options...
seriously disabled Posted October 21, 2009 Author Share Posted October 21, 2009 (edited) 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 Link to comment Share on other sites More sharing options...
ajb Posted October 21, 2009 Share Posted October 21, 2009 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. Link to comment Share on other sites More sharing options...
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