6533b835fe1ef96bd129f688

RESEARCH PRODUCT

Envelopes of open sets and extending holomorphic functions on dual Banach spaces

Ondřej F. K. KalendaDomingo GarcíaManuel Maestre

subject

Pure mathematicsAlgebra of holomorphic functionsConvex setBanach spaceOpen set46E5046B10Balanced setFOS: MathematicsAbsolutely convex setComplex Variables (math.CV)MathematicsConvex analysisDiscrete mathematicsMathematics - Complex VariablesApplied MathematicsFunctional Analysis (math.FA)46E50; 46B20; 46B10Mathematics - Functional Analysis46B20Absolutely convex setInterpolation spaceReflexive spaceAnalysisBoundedly regular setDual pair

description

We investigate certain envelopes of open sets in dual Banach spaces which are related to extending holomorphic functions. We give a variety of examples of absolutely convex sets showing that the extension is in many cases not possible. We also establish connections to the study of iterated weak* sequential closures of convex sets in the dual of separable spaces.

yearjournalcountryeditionlanguage
2010-03-01
https://dx.doi.org/10.48550/arxiv.0905.2531