Spectrum and fine spectrum of the upper triangular triple-band matrix over some sequence spaces

2015 ◽  
Author(s):  
Feyzi Başar ◽  
Ali Karaisa
Keyword(s):  
Sequence Spaces ◽  
Band Matrix ◽  
Fine Spectrum ◽  
Triple Band

scholarly journals On the fine spectrum of the generalized difference operatorB(r,s)over the sequence spacesc0andc

2005 ◽  
Vol 2005 (18) ◽  
pp. 3005-3013 ◽  
Author(s):  
Bilâl Altay ◽  
Feyzı Başar
Keyword(s):  
Difference Operator ◽  
Sequence Spaces ◽  
Band Matrix ◽  
Fine Spectrum ◽  
Special Cases ◽  
The Difference ◽  
The Right

We determine the fine spectrum of the generalized difference operatorB(r,s)defined by a band matrix over the sequence spacesc0andc, and derive a Mercerian theorem. This generalizes our earlier work (2004) for the difference operatorΔ, and includes as other special cases the right shift and the Zweier matrices.

scholarly journals Almost convergent sequence spaces derived by the domain of quadruple band matrix

2020 ◽  
Vol 19 (1) ◽  
pp. 155-170
Author(s):  
Mustafa Cemil Bişgin
Keyword(s):  
Convergent Sequence ◽  
Sequence Spaces ◽  
Schauder Basis ◽  
Third Order ◽  
Difference Matrix ◽  
Order Difference ◽  
Matrix Classes ◽  
Band Matrix ◽  
Almost Convergent Sequence ◽  
Triple Band

AbstractIn this work, we construct the sequence spaces f(Q(r, s, t, u)), f0(Q(r, s, t, u)) and fs(Q(r, s, t, u)), where Q(r, s, t, u) is quadruple band matrix which generalizes the matrices Δ3, B(r, s, t), Δ2, B(r, s) and Δ, where Δ3, B(r, s, t), Δ2, B(r, s) and Δ are called third order difference, triple band, second order difference, double band and difference matrix, respectively. Also, we prove that these spaces are BK-spaces and are linearly isomorphic to the sequence spaces f, f0 and fs, respectively. Moreover, we give the Schauder basis and β, γ-duals of those spaces. Lastly, we characterize some matrix classes related to those spaces.

scholarly journals Some Spectral Aspects of the Operator over the Sequence Spaces and

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
S. Dutta ◽  
P. Baliarsingh
Keyword(s):  
Difference Operator ◽  
Main Idea ◽  
Sequence Spaces ◽  
Difference Operators ◽  
Positive Real ◽  
Residual Spectrum ◽  
Band Matrix ◽  
Fine Spectrum ◽  
Special Cases ◽  
The Difference

The main idea of the present paper is to compute the spectrum and the fine spectrum of the generalized difference operator over the sequence spaces . The operator denotes a triangular sequential band matrix defined by with for , where or , ; the set nonnegative integers and is either a constant or strictly decreasing sequence of positive real numbers satisfying certain conditions. Finally, we obtain the spectrum, the point spectrum, the residual spectrum, and the continuous spectrum of the operator over the sequence spaces and . These results are more general and comprehensive than the spectrum of the difference operators , , , , and and include some other special cases such as the spectrum of the operators , , and over the sequence spaces or .

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.

scholarly journals Domain of the Double Sequential Band Matrix in the Sequence Space

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Havva Nergiz ◽  
Feyzi Başar
Keyword(s):  
Sequence Space ◽  
Sequence Spaces ◽  
Schauder Basis ◽  
Matrix Transformations ◽  
Difference Matrix ◽  
Band Matrix ◽  
Alpha Beta

The sequence space was introduced by Maddox (1967). Quite recently, the domain of the generalized difference matrix in the sequence space has been investigated by Kirişçi and Başar (2010). In the present paper, the sequence space of nonabsolute type has been studied which is the domain of the generalized difference matrix in the sequence space . Furthermore, the alpha-, beta-, and gamma-duals of the space have been determined, and the Schauder basis has been given. The classes of matrix transformations from the space to the spaces ,candc0have been characterized. Additionally, the characterizations of some other matrix transformations from the space to the Euler, Riesz, difference, and so forth sequence spaces have been obtained by means of a given lemma. The last section of the paper has been devoted to conclusion.

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.

Sign in / Sign up

Export Citation Format

Share Document