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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) vol.34 no.2 Antofagasta jun. 2015

http://dx.doi.org/10.4067/S0716-09172015000200001 

Spectrum and fine spectrum of the upper triangular matrix U(r, s) over the sequence spaces

Binod Chandra Tripathy

Institute of Advanced Study in Science and Technology

Rituparna Das

Sikkim Manipal Institute of Technology

India 


ABSTRACT

Fine spectra of various matrix operators on different sequence spaces have been investigated by several authors. Recently, some authors have determined the approximate point spectrum, the defect spectrum and the compression spectrum of various matrix operators on different sequence spaces. Here in this article we have determined the spectrum and fine spectrum of the upper triangular matrix U(r,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 U(r,s) on the sequence space cs.

Keywords and Phrases : Spectrum of an operator ; matrix mapping; sequence space.

AMS Classification No.: 47A10, 47B37.


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Binod Chandra Tripathy

Mathematical Sciences Division

Institute of Advanced Study in Science and Technology Guwahati-781035, Assam,

India

e-mail : tripathybc2rediffmail.com and

Rituparna Das

Department of Mathematics

Sikkim Manipal Institute of Technology

Sikkim-737136,

India

e-mail : rituparnadas_ghy@rediffmail.com

Received : July 2014. Accepted : November 2014

 

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