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• W1971170026 abstract "This note gives a characterization of BK spaces that contain isomorphic copies of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=c 0> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msub> <mml:mi>c</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:mrow> <mml:annotation encoding=application/x-tex>{c_0}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> in terms of matrix maps and a sufficient condition for a matrix map from <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=l Subscript normal infinity> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msub> <mml:mi>l</mml:mi> <mml:mi mathvariant=normal>∞<!-- ∞ --></mml:mi> </mml:msub> </mml:mrow> <mml:annotation encoding=application/x-tex>{l_infty }</mml:annotation> </mml:semantics> </mml:math> </inline-formula> into a BK space to be a compact operator. The primary tool used in this note is the Bessaga-Pelczynski characterization of Banach spaces which contain isomorphic copies of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=c 0> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msub> <mml:mi>c</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:mrow> <mml:annotation encoding=application/x-tex>{c_0}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. It is shown that weakly compact matrix maps on <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=l Subscript normal infinity> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msub> <mml:mi>l</mml:mi> <mml:mi mathvariant=normal>∞<!-- ∞ --></mml:mi> </mml:msub> </mml:mrow> <mml:annotation encoding=application/x-tex>{l_infty }</mml:annotation> </mml:semantics> </mml:math> </inline-formula> are compact and that, if <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 a BK space such that there is a matrix <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper A> <mml:semantics> <mml:mi>A</mml:mi> <mml:annotation encoding=application/x-tex>A</mml:annotation> </mml:semantics> </mml:math> </inline-formula> such that <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=c 0 subset-of-or-equal-to upper E Subscript upper A> <mml:semantics> <mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msub> <mml:mi>c</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:mrow> <mml:mo>⊆<!-- ⊆ --></mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msub> <mml:mi>E</mml:mi> <mml:mi>A</mml:mi> </mml:msub> </mml:mrow> </mml:mrow> <mml:annotation encoding=application/x-tex>{c_0} subseteq {E_A}</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 E Subscript upper A> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msub> <mml:mi>E</mml:mi> <mml:mi>A</mml:mi> </mml:msub> </mml:mrow> <mml:annotation encoding=application/x-tex>{E_A}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is not strongly conull, then <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> must contain an isomorphic copy of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=c 0> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msub> <mml:mi>c</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:mrow> <mml:annotation encoding=application/x-tex>{c_0}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>." @default.
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• W1971170026 date "1991-01-01" @default.
• W1971170026 modified "2023-09-26" @default.
• W1971170026 title "Matrix maps and the isomorphic structure of BK spaces" @default.
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• W1971170026 doi "https://doi.org/10.1090/s0002-9939-1991-1034884-8" @default.
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