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• W2068394199 abstract "The Radon-Nikodym property for the Banach algebras <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper A Subscript p Superscript r Baseline left-parenthesis upper G right-parenthesis equals upper A Subscript p Baseline intersection upper L Superscript r Baseline left-parenthesis upper G right-parenthesis> <mml:semantics> <mml:mrow> <mml:msubsup> <mml:mi>A</mml:mi> <mml:mi>p</mml:mi> <mml:mi>r</mml:mi> </mml:msubsup> <mml:mo stretchy=false>(</mml:mo> <mml:mi>G</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>A</mml:mi> <mml:mi>p</mml:mi> </mml:msub> <mml:mo>∩<!-- ∩ --></mml:mo> <mml:msup> <mml:mi>L</mml:mi> <mml:mi>r</mml:mi> </mml:msup> <mml:mo stretchy=false>(</mml:mo> <mml:mi>G</mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>A_p^r(G)=A_pcap L^r(G)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, where <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper A 2 left-parenthesis upper G right-parenthesis> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi>A</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mo stretchy=false>(</mml:mo> <mml:mi>G</mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>A_2(G)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is the Fourier algebra, is investigated. A complete solution is given for amenable groups <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper G> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding=application/x-tex>G</mml:annotation> </mml:semantics> </mml:math> </inline-formula> if <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=1 greater-than p greater-than normal infinity> <mml:semantics> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>></mml:mo> <mml:mi>p</mml:mi> <mml:mo>></mml:mo> <mml:mi mathvariant=normal>∞<!-- ∞ --></mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>1>p>infty</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and for arbitrary <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper G> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding=application/x-tex>G</mml:annotation> </mml:semantics> </mml:math> </inline-formula> if <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=p equals 2> <mml:semantics> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> <mml:annotation encoding=application/x-tex>p=2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper A 2 left-parenthesis upper G right-parenthesis> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi>A</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mo stretchy=false>(</mml:mo> <mml:mi>G</mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>A_2(G)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> has a multiplier bounded approximate identity. The results are new even for <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper G equals double-struck upper R Superscript n> <mml:semantics> <mml:mrow> <mml:mi>G</mml:mi> <mml:mo>=</mml:mo> <mml:msup> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=double-struck>R</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msup> </mml:mrow> <mml:annotation encoding=application/x-tex>G=mathbb {R}^n</mml:annotation> </mml:semantics> </mml:math> </inline-formula>." @default.
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• W2068394199 date "2011-04-22" @default.
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• W2068394199 title "The Radon-Nikodym property for some Banach algebras related to the Fourier algebra" @default.
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