# The spectrum and some subdivisions of the spectrum of discrete generalized Cesàro operators on ℓ p $\ell_{p}$ ( 1 < p < ∞ $1< p<\infty$ )

The spectrum and some subdivisions of the spectrum of discrete generalized Cesàro operators on... The discrete generalized Cesàro matrix A t = ( a n k ) $A_{t}= ( a_{nk} )$ is the triangular matrix with nonzero entries a n k = t n − k / ( n + 1 ) $a_{nk}=t^{n-k}/ ( n+1 )$ , where t ∈ [ 0 , 1 ] $t\in [ 0,1 ]$ . In this paper, boundedness, compactness, spectra, the fine spectra and subdivisions of the spectra of discrete generalized Cesàro operator on ℓ p $\ell_{p}$ ( 1 < p < ∞ $1< p<\infty$ ) have been determined. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Inequalities and Applications Springer Journals

# The spectrum and some subdivisions of the spectrum of discrete generalized Cesàro operators on ℓ p $\ell_{p}$ ( 1 < p < ∞ $1< p<\infty$ )

, Volume 2017 (1) – Aug 22, 2017
13 pages
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Publisher
Springer International Publishing
Copyright
Copyright © 2017 by The Author(s)
Subject
Mathematics; Analysis; Applications of Mathematics; Mathematics, general
eISSN
1029-242X
D.O.I.
10.1186/s13660-017-1464-2
Publisher site
See Article on Publisher Site

### Abstract

The discrete generalized Cesàro matrix A t = ( a n k ) $A_{t}= ( a_{nk} )$ is the triangular matrix with nonzero entries a n k = t n − k / ( n + 1 ) $a_{nk}=t^{n-k}/ ( n+1 )$ , where t ∈ [ 0 , 1 ] $t\in [ 0,1 ]$ . In this paper, boundedness, compactness, spectra, the fine spectra and subdivisions of the spectra of discrete generalized Cesàro operator on ℓ p $\ell_{p}$ ( 1 < p < ∞ $1< p<\infty$ ) have been determined.

### Journal

Journal of Inequalities and ApplicationsSpringer Journals

Published: Aug 22, 2017

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