scholarly journals Fine Spectra of Upper Triangular Triple-Band Matrices over the Sequence Space ()

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Ali Karaisa ◽  
Feyzi Başar
Keyword(s):  
Continuous Spectrum ◽  
Sequence Space ◽  
Point Spectrum ◽  
Band Matrices ◽  
Residual Spectrum ◽  
Approximate Point Spectrum ◽  
Fine Spectrum ◽  
The Matrix ◽  
Lower Triangular ◽  
Triple Band

The fine spectra of lower triangular triple-band matrices have been examined by several authors (e.g., Akhmedov (2006), Başar (2007), and Furken et al. (2010)). Here we determine the fine spectra of upper triangular triple-band matrices over the sequence space . The operator on sequence space on is defined by , where , with . In this paper we have obtained the results on the spectrum and point spectrum for the operator on the sequence space . Further, the results on continuous spectrum, residual spectrum, and fine spectrum of the operator on the sequence space are also derived. Additionally, we give the approximate point spectrum, defect spectrum, and compression spectrum of the matrix operator over the space and we give some applications.

scholarly journals On the fine spectrum of generalized upper triangular triple-band matrices (Δ2uvw)t over the sequence space l1

Filomat ◽  
2016 ◽  
Vol 30 (5) ◽  
pp. 1363-1373 ◽  
Author(s):  
Selma Altundağ ◽  
Merve Abay
Keyword(s):  
Sequence Space ◽  
Point Spectrum ◽  
Matrix Operator ◽  
Band Matrices ◽  
Approximate Point Spectrum ◽  
Band Matrix ◽  
Fine Spectrum ◽  
The Matrix ◽  
Triple Band

In this work, we determine the fine spectrum of the matrix operator (?2uvw)t which is defined generalized upper triangular triple band matrix on l1. Also, we give the approximate point spectrum, defect spectrum and compression spectrum of the matrix operator (?2uvw)t on l1.

Spectra and Fine Spectra of Lower Triangular Double-Band Matrices as Operators on Lp (1 ≤ p < ∞)

2015 ◽  
Vol 65 (5) ◽  
Author(s):  
Ali M. Akhmedov ◽  
Saad R. El-Shabrawy
Keyword(s):  
Continuous Spectrum ◽  
Point Spectrum ◽  
Band Matrices ◽  
Residual Spectrum ◽  
Band Matrix ◽  
The Matrix ◽  
Lower Triangular

AbstractLet Δa,b denote an infinite lower triangular double-band matrix. In this paper, the spectrum, the point spectrum, the continuous spectrum and the residual spectrum of the matrix Δ

scholarly journals Fine Spectra of Upper Triangular Double-Band Matrices over the Sequence Space ,

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Ali Karaisa
Keyword(s):  
Sequence Space ◽  
Point Spectrum ◽  
Real Numbers ◽  
Band Matrices ◽  
Approximate Point Spectrum ◽  
Band Matrix ◽  
Fine Spectrum ◽  
The Matrix ◽  
Convergent Sequences

The operator on sequence space on is defined , where , and and are two convergent sequences of nonzero real numbers satisfying certain conditions, where . The main purpose of this paper is to determine the fine spectrum with respect to the Goldberg's classification of the operator defined by a double sequential band matrix over the sequence space . Additionally, we give the approximate point spectrum, defect spectrum, and compression spectrum of the matrix operator over the space .

scholarly journals On the Fine Spectrum of the Operator Defined by the Lambda Matrix over the Spaces of Null and Convergent Sequences

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Medine Yeşilkayagil ◽  
Feyzi Başar
Keyword(s):  
Point Spectrum ◽  
Sequence Spaces ◽  
Matrix Operator ◽  
Regular Matrix ◽  
Approximate Point Spectrum ◽  
Fine Spectrum ◽  
New Development ◽  
The Matrix ◽  
Convergent Sequences

The main purpose of this paper is to determine the fine spectrum with respect to Goldberg's classification of the operator defined by the lambda matrix over the sequence spaces andc. As a new development, we give the approximate point spectrum, defect spectrum, and compression spectrum of the matrix operator on the sequence spaces andc. Finally, we present a Mercerian theorem. Since the matrix is reduced to a regular matrix depending on the choice of the sequence having certain properties and its spectrum is firstly investigated, our work is new and the results are comprehensive.

scholarly journals On the Spectral Properties of the Weighted Mean Difference Operator Gu,v;Δ over the Sequence Space ℓ1

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
P. Baliarsingh ◽  
S. Dutta
Keyword(s):  
Sequence Space ◽  
Difference Operator ◽  
Point Spectrum ◽  
Weighted Mean Difference ◽  
Mean Difference ◽  
Weighted Mean ◽  
Residual Spectrum ◽  
Fine Spectrum ◽  
Special Cases ◽  
The Difference

In the present work the generalized weighted mean difference operator Gu,v;Δ has been introduced by combining the generalized weighted mean and difference operator under certain special cases of sequences u=(uk) and v=(vk). For any two sequences u and v of either constant or strictly decreasing real numbers satisfying certain conditions the difference operator Gu,v;Δ is defined by (G(u,v;Δ)x)k=∑i=0k‍ukvi(xi-xi-1) with xk=0 for all k<0. Furthermore, we compute the spectrum and the fine spectrum of the operator Gu,v;Δ over the sequence space l1. In fact, we determine the spectrum, the point spectrum, the residual spectrum, and the continuous spectrum of this operator on the sequence space l1.

scholarly journals Spectrum and fine spectrum of the Zweier matrix over the sequence space cs

2017 ◽  
Vol 35 (2) ◽  
pp. 209 ◽  
Author(s):  
Rituparna Das
Keyword(s):  
Sequence Space ◽  
Point Spectrum ◽  
Approximate Point Spectrum ◽  
Fine Spectrum ◽  
Further Development

In this article we have determined the spectrum and fine spectrum of the Zweier matrix Z_s on the sequence space cs. In a further development, we have also determined the approximate point spectrum, the defect spectrum and the compression spectrum of the operator Z_s  on the sequence space cs.

scholarly journals On The Fine Spectrum of Generalized Lower Triangular Double Band Matrices Over The Sequence Space

2016 ◽  
Vol 37 (3) ◽  
pp. 281 ◽  
Author(s):  
Nuh DURNA ◽  
Mustafa YILDIRIM ◽  
Çağrı ÜNAL
Keyword(s):  
Sequence Space ◽  
Band Matrices ◽  
Fine Spectrum ◽  
Lower Triangular
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