Date & Time: Thursday, February 11, 2010, 16:00-17:00
Venue: Ramanujan Hall
Title: Nuclearity and Hilbert Spaces
Speaker: Amin Sofi, University of Kashmir
Abstract: As objects of study in functional analysis, Hilbert spaces stand out as special objects in view of a rich geometrical structure they possess as Banach spaces. On the other hand, nuclear spaces (a'la Grothedieck) come across as the most beautiful objects on account of their rich structural properties amongst Frechet spaces. It is remarkable that, despite their mutually exclusive character, there is an underlying commonality of approach to these disparate classes of objects in that they crop up in certain situations involving a single phenomenon - the phenomenon of finite dimensionality - which, by definition, is a generic term for those properties which are valid in finite dimensional Banach spaces and fail in infinite dimension. We shall talk about certain interesting aspects of this phenomenon and point out the ways in which it leads to the consideration of nuclear spaces on the one hand and to Hilbert spaces on the other. The discussion will be carried out mainly in the setting of vector measures.