The matrix domain and the spectra of a generalized difference operator

Jian Meng; Liquan Mei

doi:10.1016/j.jmaa.2018.10.051

The matrix domain and the spectra of a generalized difference operator

Jian Meng
, Liquan Mei

School of Mathematics and Statistics

Xi'an Jiaotong University

Research output: Contribution to journal › Article › peer-review

26 Scopus citations

Abstract

In this paper, some results of the generalized difference operator B_v ^(m) are studied. The Euler difference sequence spaces e₀ ^t(B_v ^(m)) and e_c ^t(B_v ^(m)) are introduced. Furthermore, some functional properties, α-, β- and γ-duals of these sequence spaces are examined. Finally, the sets of the spectrum, the point spectrum, the residual spectrum and the continuous spectrum of the operator B_v ^(m) on the space ℓ₁ are given.

Original language	English
Pages (from-to)	1095-1107
Number of pages	13
Journal	Journal of Mathematical Analysis and Applications
Volume	470
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2018.10.051
State	Published - 15 Feb 2019

Keywords

Difference operator
Dual space
Matrix domain
Spectral aspect

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10.1016/j.jmaa.2018.10.051

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title = "The matrix domain and the spectra of a generalized difference operator",

abstract = "In this paper, some results of the generalized difference operator Bv (m) are studied. The Euler difference sequence spaces e0 t(Bv (m)) and ec t(Bv (m)) are introduced. Furthermore, some functional properties, α-, β- and γ-duals of these sequence spaces are examined. Finally, the sets of the spectrum, the point spectrum, the residual spectrum and the continuous spectrum of the operator Bv (m) on the space ℓ1 are given.",

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N2 - In this paper, some results of the generalized difference operator Bv (m) are studied. The Euler difference sequence spaces e0 t(Bv (m)) and ec t(Bv (m)) are introduced. Furthermore, some functional properties, α-, β- and γ-duals of these sequence spaces are examined. Finally, the sets of the spectrum, the point spectrum, the residual spectrum and the continuous spectrum of the operator Bv (m) on the space ℓ1 are given.

AB - In this paper, some results of the generalized difference operator Bv (m) are studied. The Euler difference sequence spaces e0 t(Bv (m)) and ec t(Bv (m)) are introduced. Furthermore, some functional properties, α-, β- and γ-duals of these sequence spaces are examined. Finally, the sets of the spectrum, the point spectrum, the residual spectrum and the continuous spectrum of the operator Bv (m) on the space ℓ1 are given.

KW - Difference operator

KW - Dual space

KW - Matrix domain

KW - Spectral aspect

UR - https://www.scopus.com/pages/publications/85055042497

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DO - 10.1016/j.jmaa.2018.10.051

M3 - 文章

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SP - 1095

EP - 1107

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

The matrix domain and the spectra of a generalized difference operator

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Keywords

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