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• W1877332511 abstract "For a Banach algebra <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=German upper A> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=fraktur>A</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>mathfrak {A}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, amenability of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=German upper A Superscript asterisk asterisk> <mml:semantics> <mml:msup> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=fraktur>A</mml:mi> </mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo>∗<!-- ∗ --></mml:mo> <mml:mo>∗<!-- ∗ --></mml:mo> </mml:mrow> </mml:msup> <mml:annotation encoding=application/x-tex>mathfrak {A}^{**}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> necessitates amenability of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=German upper A> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=fraktur>A</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>mathfrak {A}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, and similarly for weak amenability provided <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=German upper A> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=fraktur>A</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>mathfrak {A}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a left ideal in <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=German upper A Superscript asterisk asterisk> <mml:semantics> <mml:msup> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=fraktur>A</mml:mi> </mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo>∗<!-- ∗ --></mml:mo> <mml:mo>∗<!-- ∗ --></mml:mo> </mml:mrow> </mml:msup> <mml:annotation encoding=application/x-tex>mathfrak {A}^{**}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. For <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=German upper G> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=fraktur>G</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>mathfrak {G}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> a locally compact group, indeed more generally, <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper L Superscript 1 Baseline left-parenthesis German upper G right-parenthesis Superscript asterisk asterisk> <mml:semantics> <mml:mrow> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>1</mml:mn> </mml:msup> <mml:mo stretchy=false>(</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=fraktur>G</mml:mi> </mml:mrow> <mml:msup> <mml:mo stretchy=false>)</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo>∗<!-- ∗ --></mml:mo> <mml:mo>∗<!-- ∗ --></mml:mo> </mml:mrow> </mml:msup> </mml:mrow> <mml:annotation encoding=application/x-tex>L^1(mathfrak {G})^{**}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is amenable if and only if <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=German upper G> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=fraktur>G</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>mathfrak {G}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is finite. If <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper L Superscript 1 Baseline left-parenthesis German upper G right-parenthesis Superscript asterisk asterisk> <mml:semantics> <mml:mrow> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>1</mml:mn> </mml:msup> <mml:mo stretchy=false>(</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=fraktur>G</mml:mi> </mml:mrow> <mml:msup> <mml:mo stretchy=false>)</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo>∗<!-- ∗ --></mml:mo> <mml:mo>∗<!-- ∗ --></mml:mo> </mml:mrow> </mml:msup> </mml:mrow> <mml:annotation encoding=application/x-tex>L^1(mathfrak {G})^{**}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is weakly amenable, then <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper M left-parenthesis German upper G right-parenthesis> <mml:semantics> <mml:mrow> <mml:mi>M</mml:mi> <mml:mo stretchy=false>(</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=fraktur>G</mml:mi> </mml:mrow> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>M(mathfrak {G})</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is weakly amenable." @default.
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• W1877332511 date "1996-01-01" @default.
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• W1877332511 title "Amenability and weak amenability of second conjugate Banach algebras" @default.
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