A characterization of nuclear operators on spaces of vector-valued continuous functions with the strict topology

IF 0.8 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society Pub Date : 2024-02-29 DOI:10.1090/proc/16805

Juliusz Stochmal

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Let <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper C Subscript b Baseline left-parenthesis upper X comma upper E right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi>C</mml:mi> <mml:mi>b</mml:mi> </mml:msub> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>X</mml:mi> <mml:mo>,</mml:mo> <mml:mi>E</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">C_b(X,E)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> denote the space of <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>-valued bounded continuous functions on <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X\"> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding=\"application/x-tex\">X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and let <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"beta\"> <mml:semantics> <mml:mi>β</mml:mi> <mml:annotation encoding=\"application/x-tex\">\\beta</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be the strict topology on this space. 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引用次数: 0

Abstract

Let X X be a completely regular Hausdorff space, let E E and F F denote Banach spaces. Let C b ( X , E ) C_b(X,E) denote the space of E E -valued bounded continuous functions on X X and let β \beta be the strict topology on this space. We establish the relationship between nuclear operators T : C b ( X , E ) → F T:C_b(X,E)\rightarrow F between the locally convex space ( C b ( X , E ) , β ) (C_b(X,E),\beta ) and the Banach space F F and their representing operator-valued Borel measures.

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有严格拓扑的向量连续函数空间上核算子的表征

设 X X 是完全正则的豪斯多夫空间，设 E E 和 F F 表示巴拿赫空间。让 C b ( X , E ) C_b(X,E) 表示 X X 上 E E 有界连续函数的空间，让 β \beta 是这个空间的严格拓扑。我们建立局部凸空间 ( C b ( X , E ) , β ) (C_b(X,E),\beta ) 与巴拿赫空间 F F 之间核算子 T : C b ( X , E ) → F T:C_b(X,E)\rightarrow F 之间的关系，以及它们代表的算子值博尔量。

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来源期刊

Proceedings of the American Mathematical Society 数学-数学

CiteScore

1.70

自引率

10.00%

发文量

207

审稿时长

2-4 weeks

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