Search results for "46E50"

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Gleason parts for algebras of holomorphic functions on the ball of $\mathbf{c_0}$

2019

For a complex Banach space $X$ with open unit ball $B_X,$ consider the Banach algebras $\mathcal H^\infty(B_X)$ of bounded scalar-valued holomorphic functions and the subalgebra $\mathcal A_u(B_X)$ of uniformly continuous functions on $B_X.$ Denoting either algebra by $\mathcal A,$ we study the Gleason parts of the set of scalar-valued homomorphisms $\mathcal M(\mathcal A)$ on $\mathcal A.$ Following remarks on the general situation, we focus on the case $X = c_0.$

Mathematics - Functional AnalysisMathematics::Functional AnalysisFOS: Mathematics46J15 30H50 46E50 30H05Functional Analysis (math.FA)
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Envelopes of open sets and extending holomorphic functions on dual Banach spaces

2010

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.

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
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