A meeting of the North British Functional Analysis Seminar was held at the University of Lancaster on May 25th 2009.
Abstract: Let D be a fundamental set in a Banach space X. Greedy algorithms provide an intuitively appealing method for approximating a given vector by a linear combination of n vectors belonging to D. The convergence of one such ``Pure Greedy Algorithm'' in Hilbert space is well understood. We consider some natural generalizations of this Hilbert space algorithm to the Banach space setting and examine their convergence properties with respect to either the norm or the weak topologies. We also consider the important case in which D is a basis for X, so that each vector in X has a series representation with respect to the basis. Here the most natural approximation method is to select the n largest basis coefficients in absolute value. We shall consider the convergence properties of this ``Thresholding Greedy Algorithm'' and discuss the existence of bases for which algorithms of this type are effective.
This was preceded by an introductory talk for postgraduate students by Dr Andras Zsak at 1.15 p.m. on An introduction to bases in Banach spaces.
All talks took place in Lecture Theatre A54 in the Postgraduate Statistics Centre.
There was a dinner in honour of Graham Jameson in the evening, and the Conference on Banach spaces, operators and inequalities in honour of Graham Jameson took place on the following day.
All interested were welcome to attend.
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Some support was available for graduate students, on emailing Stuart White, email@example.com, for information.
NBFAS is registered with the Charity Commissioners. Reg. No: 313424.
The address of this page is http://www.maths.leeds.ac.uk/nbfas/lanc09.html
Last updated on May 27th 2009 by Jonathan Partington