Bibliography for topologies defined by a family of seminorms - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-20T09:54:52Z http://mathoverflow.net/feeds/question/9538 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/9538/bibliography-for-topologies-defined-by-a-family-of-seminorms Bibliography for topologies defined by a family of seminorms Learner 2009-12-22T12:25:37Z 2010-03-12T11:27:27Z <p>Hello</p> <p>I am trying to learn more about Fréchet spaces (in order to study the theory of distributions) and was wondering what people thought was the best resource.</p> <p>Thank you very much.</p> http://mathoverflow.net/questions/9538/bibliography-for-topologies-defined-by-a-family-of-seminorms/9553#9553 Answer by Xabier DomÃ­nguez for Bibliography for topologies defined by a family of seminorms Xabier DomÃ­nguez 2009-12-22T18:16:59Z 2009-12-22T18:16:59Z <p>I don't know much about distributions but if you're entering this area with such a motivation, maybe you could use Horvath's book "Topological vector spaces and distributions". The first part is a fine introduction to locally convex space theory in itself, and the presentation of this (rather standard) material should be convenient for anybody interested on the final chapter -- distributions.</p> <p>By the way, a linear topology on a vector space which is defined using a family of seminorms is in general a locally convex topology, not necessarily metrizable (Fréchet spaces are metrizable and complete locally convex spaces). </p> http://mathoverflow.net/questions/9538/bibliography-for-topologies-defined-by-a-family-of-seminorms/17971#17971 Answer by Ulrich Pennig for Bibliography for topologies defined by a family of seminorms Ulrich Pennig 2010-03-12T10:56:25Z 2010-03-12T10:56:25Z <p>I just had a look at </p> <blockquote> <p>Topological Vector Spaces, Distributions and Kernels</p> </blockquote> <p>by Francois Treves. It is divided into three parts:</p> <p><strong>I Topological Vector Spaces. Spaces of Funtions</strong></p> <ul> <li>covering: basic material about locally convex spaces and Frechet spaces (with a lot of examples)</li> </ul> <p><strong>II Duality, Spaces of Distributions</strong></p> <ul> <li>topologies on Duals, transposes of linear maps, convolution, barreled spaces </li> </ul> <p><strong>III Tensor Products. Kernels</strong></p> <ul> <li>injective and projective tensor products and their relation to bilinear forms, nuclear spaces, nuclear mappings, Schwartz kernel theorem and applications</li> </ul> <p>From the first sight, this looks like a good place to start if you are already familiar with functional analysis on Banach and Hilbert spaces. </p>