Probabilistic Operator Algebra Seminar: Schauder bases in Banach lattices
Seminar | August 28 | 3:45-5:45 p.m. | 748 Evans Hall
Mitchell Taylor, UC Berkeley
The order structure of a Banach lattice gives rise to several natural convergences. In this talk we begin by reviewing the essential results on Banach lattices, and then discuss recent research on basic sequences in such spaces. The basic sequences we are interested in are those whose partial sums converge not only in norm, but also in order. We show that this class of bases can be characterized by a natural modification of the standard basis inequality, and discuss some of the more unexpected corollaries. This is a joint project with V.G. Troitsky ; the results extend and unify those of A. Gumenchuk, O. Karlova and M. Popov, Order Schauder bases in Banach lattices, J. Funct. Anal. (2015).