IISER - TVM
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Indian Institute of Science Education and Research Thiruvananthapuram
GST ID : 32AAAJI0299R1ZS

IISER TVM Decennial Celebrations

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Seminars

Delta-convergence: an alternative approach to weak compactness

A point x in a metric space is called a Delta-limit of a sequence x_n if for any other point y, d(x_n,y)>d(x_n,x)+o(1).Surprisingly,  this is an equivalent definition of weak limit in Hilbert spaces and l^p, but in many other Banach spaces it is not. Similarly to weak convergence, a bounded sequence has a convergent subsequence provided that the space is asymptotically complete. Asymptotic completeness  is a property vaguely similar to reflexivity, and like reflexivity it is satisfied by uniformly convex Banach spaces. This remains true also in metric spaces under a suitable generalization. Delta-limits of sequences are also their asymptotic centers, which implies that Delta-convergence is a natural mode of convergence for iterations of non-expansive maps.

Date and Time: 2016/01/07 14:00 Venue: Seminar Room (219)
Speaker: Dr. Cyril Tintarev Speaker - Affiliations: Uppsala University