有界Φ-variation函数的Banach代数上的乘法算子

IF 2 3区数学 Q1 MATHEMATICS

Demonstratio Mathematica Pub Date : 2022-01-01 DOI:10.1515/dema-2022-0162

M. Bracamonte, J. Ereú, L. Marchan

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引用次数: 0

摘要

设A Φ (K) {{\mathbb{A}}} ＿ {\Phi}\left({\bf{K}})是定义在紧集K上的有界Φ \Phi变分函数的Banach代数{\bf{K}}，h h是定义在K上的函数，M h {\bf{K}}M＿h{是由h h引起的乘法算子。在本文中，我们确定了h h是闭值域、有限秩或紧的算子时}h{ h必须满足的条件。我们还描述了h h必须满足的条件，使M h M＿h}成为{Fredholm}算子。{}{}{}

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Multiplication operators on the Banach algebra of bounded Φ-variation functions on compact subsets of ℂ

Abstract Let A Φ ( K ) {{\mathbb{A}}}_{\Phi }\left({\bf{K}}) be the Banach algebra of bounded Φ \Phi -variation functions defined on a compact set K {\bf{K}} in the complex plane, h h a function defined on K {\bf{K}} , and M h {M}_{h} a multiplication operator induced by h h . In this article, we determine the conditions that h h must satisfy for M h {M}_{h} to be an operator that has closed range, finite rank or is compact. We also characterize the conditions that h h must satisfy for M h {M}_{h} to be a Fredholm operator.

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来源期刊

Demonstratio Mathematica MATHEMATICS-

CiteScore

2.40

自引率

5.00%

发文量

审稿时长

35 weeks

期刊介绍： Demonstratio Mathematica publishes original and significant research on topics related to functional analysis and approximation theory. Please note that submissions related to other areas of mathematical research will no longer be accepted by the journal. The potential topics include (but are not limited to): -Approximation theory and iteration methods- Fixed point theory and methods of computing fixed points- Functional, ordinary and partial differential equations- Nonsmooth analysis, variational analysis and convex analysis- Optimization theory, variational inequalities and complementarity problems- For more detailed list of the potential topics please refer to Instruction for Authors. The journal considers submissions of different types of articles. "Research Articles" are focused on fundamental theoretical aspects, as well as on significant applications in science, engineering etc. “Rapid Communications” are intended to present information of exceptional novelty and exciting results of significant interest to the readers. “Review articles” and “Commentaries”, which present the existing literature on the specific topic from new perspectives, are welcome as well.