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• W4283591219 abstract "The algebra <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper H Superscript normal infinity Baseline left-parenthesis upper D right-parenthesis> <mml:semantics> <mml:mrow> <mml:msup> <mml:mi>H</mml:mi> <mml:mi mathvariant=normal>∞<!-- ∞ --></mml:mi> </mml:msup> <mml:mo stretchy=false>(</mml:mo> <mml:mi>D</mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>H^infty (D)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of bounded holomorphic functions on <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper D subset-of double-struck upper C> <mml:semantics> <mml:mrow> <mml:mi>D</mml:mi> <mml:mo>⊂<!-- ⊂ --></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>Dsubset mathbb {C}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is projective free for a wide class of infinitely connected domains. In particular, for such <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper D> <mml:semantics> <mml:mi>D</mml:mi> <mml:annotation encoding=application/x-tex>D</mml:annotation> </mml:semantics> </mml:math> </inline-formula> every rectangular left-invertible matrix with entries in <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper H Superscript normal infinity Baseline left-parenthesis upper D right-parenthesis> <mml:semantics> <mml:mrow> <mml:msup> <mml:mi>H</mml:mi> <mml:mi mathvariant=normal>∞<!-- ∞ --></mml:mi> </mml:msup> <mml:mo stretchy=false>(</mml:mo> <mml:mi>D</mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>H^infty (D)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> can be extended in this class of matrices to an invertible square matrix. This follows from a new result on the structure of the maximal ideal space of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper H Superscript normal infinity Baseline left-parenthesis upper D right-parenthesis> <mml:semantics> <mml:mrow> <mml:msup> <mml:mi>H</mml:mi> <mml:mi mathvariant=normal>∞<!-- ∞ --></mml:mi> </mml:msup> <mml:mo stretchy=false>(</mml:mo> <mml:mi>D</mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>H^infty (D)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> asserting that its covering dimension is <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=2> <mml:semantics> <mml:mn>2</mml:mn> <mml:annotation encoding=application/x-tex>2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and the second Čech cohomology group is trivial." @default.
• W4283591219 created "2022-06-28" @default.
• W4283591219 creator A5004010557 @default.
• W4283591219 date "2022-06-27" @default.
• W4283591219 modified "2023-10-14" @default.
• W4283591219 title "Projective free algebras of bounded holomorphic functions on infinitely connected domains" @default.
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• W4283591219 doi "https://doi.org/10.1090/spmj/1718" @default.
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