Weighted shift operators and extended eigenvalues

IF 1.1 Q1 MATHEMATICS

JOURNAL OF INTERDISCIPLINARY MATHEMATICS Pub Date : 2023-01-01 DOI:10.47974/jim-1516

Kareem M. Hussein, Buthainah A. Ahmed

引用次数: 0

Abstract

Let H be a Hilbert space. A complex number is named the extended eigenvalue for an operator T ∈ B(H), if there is operator not equal zero X ∈ B(H) so that: TX = mXT and X are named as extended eigen operator for an operator T opposite to m. The goal of this work is to find extended eigenvalues and extended eigen operators for shift operators J, Ja, K, Ka such that J : I2 (ℕ) → I2 (ℕ) and K : I2 (ℕ) → I2 (ℕ) defined by: Jen = e2n , and Ken = { (en/2 if n even) (0 if n odd), for all x ∈ l2(ℕ). Furthermore, the closeness of extended eigenvalues for all of these shift operators under multiplication has been proven.

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加权移位算子和扩展特征值

设H是希尔伯特空间。复数命名的扩展特征值算子T∈B (H),如果运营商不等于0 X∈B (H),这样:TX = mXT中X命名作为运营商扩展特征算子T m相反。这项工作的目标是找到特征值和特征运营商延伸为移动运营商J,是的,K, Ka, J: I2(ℕ)→I2(ℕ)和K: I2(ℕ)→I2(ℕ)定义的 : Jen = e2n,肯= {(en / 2如果n)(0如果n奇怪),对于所有x∈l2(ℕ)。进一步证明了所有这些移位算子的扩展特征值在乘法下的接近性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

JOURNAL OF INTERDISCIPLINARY MATHEMATICS MATHEMATICS-

CiteScore

2.70

自引率

23.50%

发文量

141

期刊介绍： The Journal of Interdisciplinary Mathematics (JIM) is a world leading journal publishing high quality, rigorously peer-reviewed original research in mathematical applications to different disciplines, and to the methodological and theoretical role of mathematics in underpinning all scientific disciplines. The scope is intentionally broad, but papers must make a novel contribution to the fields covered in order to be considered for publication. Topics include, but are not limited, to the following: • Interface of Mathematics with other Disciplines • Theoretical Role of Mathematics • Methodological Role of Mathematics • Interface of Statistics with other Disciplines • Cognitive Sciences • Applications of Mathematics • Industrial Mathematics • Dynamical Systems • Mathematical Biology • Fuzzy Mathematics The journal considers original research articles, survey articles, and book reviews for publication. Responses to articles and correspondence will also be considered at the Editor-in-Chief’s discretion. Special issue proposals in cutting-edge and timely areas of research in interdisciplinary mathematical research are encouraged – please contact the Editor-in-Chief in the first instance.