User anonymous - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-19T10:26:15Z http://mathoverflow.net/feeds/user/3825 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/14329/what-is-the-tensor-product-of-lp-bf-r-with-lq-bf-r What is the tensor product of $L^p(\bf R)$ with $L^q(\bf R)$? Anonymous 2010-02-06T00:05:27Z 2010-02-19T15:34:59Z <p>I'm wondering: What is the tensor product of $L^p({\bf R})$ with $L^q({\bf R})$?</p> <p>(For p=q=2, the answer clearly should be $L^2({\bf R}^2)$; for other values of $p$ and $q$, it is not at all obvious to me what $L^p({\bf R})\otimes L^q({\bf R})$ should be.)</p> http://mathoverflow.net/questions/14329/what-is-the-tensor-product-of-lp-bf-r-with-lq-bf-r Comment by Anonymous Anonymous 2010-02-06T00:41:11Z 2010-02-06T00:41:11Z @Martin: Although I'm obviously not an expert on these thinks, I'm well aware of the variety of possible norms on the tensor product. Part of my question is: Which one is the good definition in this setting? There should be a good notion in this case. In the $L^2$-case, we certainly want the Hilbert space notion of the tensor product, since this one gives a nice answer, and I expect that there is some setting which handles the $L^p \otimes L^q$-case quite well. @Yemon: Thanks. I'll take a look at this book.