巴拿赫晶格数列中的带投影和阶等式

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications Pub Date : 2024-11-12 DOI:10.1016/j.jmaa.2024.129045

David Muñoz-Lahoz

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引用次数: 0

摘要

受最近关于巴拿赫网格上正则算子空间的带投影的研究的启发，给定一个巴拿赫网格代数 A，如果乘法算子 LaRa∈Lr(A)是一个带投影，我们就说元素 a∈A+ 是一个带投影。我们在本说明中的目的是探讨这一点与阶幂（巴拿赫网格代数 A 中的元素 a，其特征值为 e，使得 0≤a≤e 且 a2=a）概念之间的关系。我们还以巴拿赫网格中心的性质为动机，重温了由巴拿赫网格代数上的标识所产生的理想的性质。

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Band projections and order idempotents in Banach lattice algebras

Motivated by recent work about band projections on spaces of regular operators over a Banach lattice, given a Banach lattice algebra A, we will say an element

a \in A_{+}

is a band projection if the multiplication operator

L_{a} R_{a} \in L_{r} (A)

is a band projection. Our aim in this note is to explore the relations between this and the notion of order idempotent (those elements a in a Banach lattice algebra A with identity e such that

0 \leq a \leq e

and

a^{2} = a

). We also revisit the properties of the ideal generated by the identity on a Banach lattice algebra, motivated by those of the centre of a Banach lattice.

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来源期刊

Journal of Mathematical Analysis and Applications 数学-数学

CiteScore

2.50

自引率

7.70%

发文量

790

审稿时长

6 months

期刊介绍： The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Papers are sought which employ one or more of the following areas of classical analysis: • Analytic number theory • Functional analysis and operator theory • Real and harmonic analysis • Complex analysis • Numerical analysis • Applied mathematics • Partial differential equations • Dynamical systems • Control and Optimization • Probability • Mathematical biology • Combinatorics • Mathematical physics.