Weighted shift operators and extended eigenvalues

Hussein, Kareem M.; Ahmed, Buthainah A.

doi:10.47974/JIM-1516

Open Access Research Article

Weighted shift operators and extended eigenvalues

^*Kareem M. HusseinCorresponding authorkmhsn780@gmail.comDepartment of Mathematics College of Science University of BaghdadBaghdad, IraqView full profile → , Buthainah A. Ahmedbuthaina.a@sc.uobaghdad.edu.iqDepartment of Mathematics College of Science University of BaghdadBaghdad, IraqView full profile →

* Corresponding author · click or hover a name for details

pp. 849–855Vol. 26Issue 5August 2023DOI: 10.47974/JIM-1516XML

Received:: 11 May 2022
Accepted:: 09 Jun 2022
Published Online:: 15 Jul 2023
Article type:: Research Article
Language:: EN
Article no.:: JIM-1516
Pages:: 849–855

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.

Keywords

Extended eigenvalues Extended eigen operators Weighted shift operators

Subject Classifications

00A0500A06

Acknowledgements

Obaid (44_icmas_h10)

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