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• W2073164619 abstract "For a locally compact group <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>, let <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper A left-parenthesis upper G right-parenthesis> <mml:semantics> <mml:mrow> <mml:mi>A</mml:mi> <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(G)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> denote its Fourier algebra and <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=ModifyingAbove upper G With caret> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mover> <mml:mi>G</mml:mi> <mml:mo stretchy=false>^<!-- ^ --></mml:mo> </mml:mover> </mml:mrow> <mml:annotation encoding=application/x-tex>hat {G}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> its dual object, i.e., the collection of equivalence classes of unitary representations of <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>. We show that the amenability constant of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper A left-parenthesis upper G right-parenthesis> <mml:semantics> <mml:mrow> <mml:mi>A</mml:mi> <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(G)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is less than or equal to <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=sup left-brace right-brace colon of degdeg left-parenthesis right-parenthesis pi colon element-of element-of pi upper G caret> <mml:semantics> <mml:mrow> <mml:mo movablelimits=true form=prefix>sup</mml:mo> <mml:mo fence=false stretchy=false>{</mml:mo> <mml:mi>deg</mml:mi> <mml:mo>⁡<!-- ⁡ --></mml:mo> <mml:mo stretchy=false>(</mml:mo> <mml:mi>π<!-- π --></mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo>:</mml:mo> <mml:mi>π<!-- π --></mml:mi> <mml:mo>∈<!-- ∈ --></mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mover> <mml:mi>G</mml:mi> <mml:mo stretchy=false>^<!-- ^ --></mml:mo> </mml:mover> </mml:mrow> <mml:mo fence=false stretchy=false>}</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>sup { deg (pi ) : pi in hat {G} }</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and that it is equal to one if and only if <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> is abelian." @default.
• W2073164619 created "2016-06-24" @default.
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• W2073164619 date "2005-10-18" @default.
• W2073164619 modified "2023-09-23" @default.
• W2073164619 title "The amenability constant of the Fourier algebra" @default.
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