| Abstract: | The order structure of a Banach lattice gives rise to several natural convergences. In this talk we discuss basic sequences in Banach lattices 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 from A. Gumenchuk, O. Karlova and M. Popov, Order Schauder bases in Banach lattices, J. Funct. Anal. (2015). |
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