On the fine spectrum of the generalized difference operator <mml:math alttext="$B(r,s)$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>B</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>r</mml:mi><mml:mo>,</mml:mo><mml:mi>s</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math> over  the sequence spaces <mml:math alttext="$c_0$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>c</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:math> and <mml:math alttext="$c$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>c</mml:mi></mml:math>

Altay, Bilâl; Başar, Feyzı

doi:https://doi.org/10.1155/IJMMS.2005.3005

International Journal of Mathematics and Mathematical Sciences

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Volume 2005 | Article ID 854658 | https://doi.org/10.1155/IJMMS.2005.3005

On the fine spectrum of the generalized difference operator B(r,s) over the sequence spaces c0 and c

Bilâl Altay¹and Feyzı Başar¹

Received27 Apr 2005

Revised15 Jul 2005

Abstract

We determine the fine spectrum of the generalized difference operator B(r,s) defined by a band matrix over the sequence spaces c0 and c, and derive a Mercerian theorem. This generalizes our earlier work (2004) for the difference operator Δ, and includes as other special cases the right shift and the Zweier matrices.

Copyright

Copyright © 2005 Bilâl Altay and Feyzı Başar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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