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• W1511601589 abstract "A Banach space <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper E> <mml:semantics> <mml:mi>E</mml:mi> <mml:annotation encoding=application/x-tex>E</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is known to be Arens regular if every continuous linear mapping from <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper E> <mml:semantics> <mml:mi>E</mml:mi> <mml:annotation encoding=application/x-tex>E</mml:annotation> </mml:semantics> </mml:math> </inline-formula> to <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper E prime> <mml:semantics> <mml:msup> <mml:mi>E</mml:mi> <mml:mo>′</mml:mo> </mml:msup> <mml:annotation encoding=application/x-tex>E’</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is weakly compact. Let <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper U> <mml:semantics> <mml:mi>U</mml:mi> <mml:annotation encoding=application/x-tex>U</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be an open subset of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper E> <mml:semantics> <mml:mi>E</mml:mi> <mml:annotation encoding=application/x-tex>E</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, and let <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper H Subscript b Baseline left-parenthesis upper U right-parenthesis> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi>H</mml:mi> <mml:mi>b</mml:mi> </mml:msub> <mml:mo stretchy=false>(</mml:mo> <mml:mi>U</mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>H_b(U)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> denote the algebra of analytic functions on <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper U> <mml:semantics> <mml:mi>U</mml:mi> <mml:annotation encoding=application/x-tex>U</mml:annotation> </mml:semantics> </mml:math> </inline-formula> which are bounded on bounded subsets of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper U> <mml:semantics> <mml:mi>U</mml:mi> <mml:annotation encoding=application/x-tex>U</mml:annotation> </mml:semantics> </mml:math> </inline-formula> lying at a positive distance from the boundary of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper U period> <mml:semantics> <mml:mrow> <mml:mi>U</mml:mi> <mml:mo>.</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>U.</mml:annotation> </mml:semantics> </mml:math> </inline-formula> We endow <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper H Subscript b Baseline left-parenthesis upper U right-parenthesis> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi>H</mml:mi> <mml:mi>b</mml:mi> </mml:msub> <mml:mo stretchy=false>(</mml:mo> <mml:mi>U</mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>H_b(U)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> with the usual Fréchet topology. <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper M Subscript b Baseline left-parenthesis upper U right-parenthesis> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi>M</mml:mi> <mml:mi>b</mml:mi> </mml:msub> <mml:mo stretchy=false>(</mml:mo> <mml:mi>U</mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>M_b(U)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> denotes the set of continuous homomorphisms <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=phi colon upper H Subscript b Baseline left-parenthesis upper U right-parenthesis right-arrow double-struck upper C> <mml:semantics> <mml:mrow> <mml:mi>ϕ<!-- ϕ --></mml:mi> <mml:mo>:</mml:mo> <mml:msub> <mml:mi>H</mml:mi> <mml:mi>b</mml:mi> </mml:msub> <mml:mo stretchy=false>(</mml:mo> <mml:mi>U</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo stretchy=false>→<!-- → --></mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=double-struck>C</mml:mi> </mml:mrow> </mml:mrow> <mml:annotation encoding=application/x-tex>phi :H_b(U) to mathbb {C}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. We study the relation between the Arens regularity of the space <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper E> <mml:semantics> <mml:mi>E</mml:mi> <mml:annotation encoding=application/x-tex>E</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and the structure of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper M Subscript b Baseline left-parenthesis upper U right-parenthesis> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi>M</mml:mi> <mml:mi>b</mml:mi> </mml:msub> <mml:mo stretchy=false>(</mml:mo> <mml:mi>U</mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>M_b(U)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>." @default.
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• W1511601589 date "1996-01-01" @default.
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• W1511601589 title "Regularity and Algebras of Analytic Functions in Infinite Dimensions" @default.
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