Complexification and tensor products of Banach spaces: an isometric result for the projective tensor norm.
Starts 14 Dec 2010 10:30
Ends 14 Dec 2010 20:00
Central European Time
Leonardo da Vinci Building Euler Lecture Hall
Strada Costiera, 11
I - 34151 Trieste (Italy)
Finding the "complexification" of a real vector space is trivial; essentially the same as obtaining the complex numbers from the real numbers. However, when complexifying a real Banach space, there are a range of choices, for a norm that fits in naturally with the norm of the real Banach space. In this talk it is proved that one of these choices has a property that one expects, namely that the complexification of the projective tensor product of any two real Banach spaces is isometrically isomorphic to the projective tensor product of their complexifications.