Spectra and fine spectra for the upper triangular band matrix U(a 0 , a 1 , a 2 ; b 0 , b 1 , b 2 ) over the sequence space c 0

Durna, Nuh; Kılıç, Rabia

doi:10.4067/s0716-09172019000100145

Cited by 3 publications

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References 12 publications

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“…In this paper, we will calculate spectral decomposition of U (a 0 , a 1 , a 2 ; b 0 , b 1 , b 2 ) matrix. U (a 0 , a 1 , a 2 ; b 0 , b 1 , b 2 ) matrix is studied in c 0 sequence space by Durna and Kılıç [9] therefore some result is omit becuse it is similar with [9].…”

Section: Introductionmentioning

confidence: 99%

On the spectrum of the upper triangular double band matrix $U(a_{0},a_{1},a_{2};b_{0},b_{1},b_{2})$ over the sequence $c$

Durna

Kılıç

2022

Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.

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The upper triangular double band matrix $U(a_{0},a_{1},a_{2};b_{0},b_{1},b_{2})$ is defined on a Banach sequence space by $U(a_{0},a_{1},a_{2};b_{0},b_{1},b_{2})(x_{n})=(a_{n}x_{n}+b_{n}x_{n+1})_{n=0}^{\infty}$where $a_{x}=a_{y},~b_{x}=b_{y}$ for $x\equiv y~(mod3)$. The class of the operator$U(a_{0},a_{1},a_{2};b_{0},b_{1},b_{2})$includes, in particular, the operator $U(r,s)$ when $a_{k}=r$ and $b_{k}=s$ for all $k\in\mathbb{N}$, with $r,s\in\mathbb{R}$ and $s\neq 0$. Also, it includes the upper difference operator; $a_{k}=1$ and $b_{k}=-1$ for all $k\in\mathbb{N}$. In this paper, we completely determine the spectrum, the fine spectrum, the approximate point spectrum, the defect spectrum, and the compression spectrum of the operator $U(a_{0},a_{1},a_{2};b_{0},b_{1},b_{2})$ over the sequence space $c$.

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Section: Introductionmentioning

confidence: 99%

On the spectrum of the upper triangular double band matrix $U(a_{0},a_{1},a_{2};b_{0},b_{1},b_{2})$ over the sequence $c$

Durna

Kılıç

2022

Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.

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Spectra of Lower Triangular Infinite Matrices Formed by Oscillatory Sequences

Mahto

Srivastava

2021

Complex Anal. Oper. Theory

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Spectra and fine spectra of the generalized upper difference operator with triple repetition Δ3ab$\begin{array}{}\displaystyle\Delta_{3}^{ab}\end{array}$ on the Hahn sequence space

Durna

Mursaleen

Kılıç

2022

Mathematica Slovaca

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The goal of this paper is to obtain the spectra and fine spectra of the matrix Δ 3 a b $\begin{array}{} \displaystyle \Delta_{3}^{ab} \end{array}$ on the Hahn space. Also, we explore some ideas of how to study the problem for a general form of the matrix, namely, the matrix Δ n a b $\begin{array}{} \displaystyle \Delta _{n}^{ab} \end{array}$ where the non-zero diagonals are the entries of a n-ary repetition sequence.

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Spectra and fine spectra for the upper triangular band matrix U(a 0 , a 1 , a 2 ; b 0 , b 1 , b 2 ) over the sequence space c 0

Abstract: The aim of this paper is to obtain the spectrum, fine spectrum, approximate point spectrum, defect spectrum and compression spectrum of the operatorSubjclass : 47A10; 47B37; 15A18.

Cited by 3 publications

References 12 publications

On the spectrum of the upper triangular double band matrix $U(a_{0},a_{1},a_{2};b_{0},b_{1},b_{2})$ over the sequence $c$

On the spectrum of the upper triangular double band matrix $U(a_{0},a_{1},a_{2};b_{0},b_{1},b_{2})$ over the sequence $c$

Spectra of Lower Triangular Infinite Matrices Formed by Oscillatory Sequences

Spectra and fine spectra of the generalized upper difference operator with triple repetition Δ3ab$\begin{array}{}\displaystyle\Delta_{3}^{ab}\end{array}$ on the Hahn sequence space

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