Some properties on extended eigenvalues and extended eigenvectors

Shaakir, Laith K.; Hijab, Anas A.

doi:10.25130/j.v24i6.898

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2023

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“…L.K. Shaakir and Anas A. Hijab [6] calculated the set of all extended eigenvalues of unilateral shift operator on the L 2 space . F. Leon and S. Petovic [7] gave a full solution to the problem of computing the extended eigenvalues for those composition operators 𝑐 𝜑 induced on the Hardy space 𝐻 2 (𝔻) by linear fractional transformations 𝜑 of the unit disk.…”

Section: Introductionmentioning

confidence: 99%

Extended Eigenvalues and Eigenoperators of Some Weighted Shift Operators

Hussein

Ahmed²

2023

Iraqi Journal of Science

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A complex number is called an extended eigenvalue for an operator on a Hilbert space H if there exists a nonzero operator such that: such is called an extended eigenoperator corresponding to. The goal of this paper is to calculate extended eigenvalues and extended eigenoperators for the weighted unilateral (Forward and Backward) shift operators. We also find an extended eigenvalues for weighted bilateral shift operator. Moreover, the closedness of extended eigenvalues for the weighted unilateral (Forward and Backward) shift operators under multiplication is proven.

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Section: Introductionmentioning

confidence: 99%