Extremity in Köthe-Bochner Function Spaces
Abstract
LetEbe a Köthe function space over a complete measurable space andXa Banach space. Recall an elementhinEis said to beorder continuousif, for any decreasing sequence {gn} inSE, ngn=0 andgn≤h implies limn→∞gn=0. We show that every denting point of the unit ball ofEis order continuous. Using this result, we prove thatfis a denting point of the unit ball ofE(X) if and only if (·)is a denting point of the unit ball of. for almost all∈supp,()/()is a denting point of the unit ball of.Suppose thatEis order continuous. We also prove that for any unit vectorfinE(X), if f(·)Xis a strongly exposed point of the unit ball ofEand for almost allt∈suppf,f(t)/f(t)Xis a strongly exposed point of the unit ball ofX, thenfis a strongly exposed point of the unit ball ofE(X). © 1998 Academic Press.
Publication Title
Journal of Mathematical Analysis and Applications
Recommended Citation
Lin, P., & Sun, H. (1998). Extremity in Köthe-Bochner Function Spaces. Journal of Mathematical Analysis and Applications, 218 (1), 136-154. https://doi.org/10.1006/jmaa.1997.5765
