Spectra and fine spectra of the upper triangular band matrix U(a; 0; b) on the Hahn sequence space

The aim of this paper is to obtain the spectra and fine spectra of the matrix (U(a;0;b)) on the Hahn space. Also, we explore some ideas of how to study the problem for a general form of the matrix, namely, the matrix (U(a_{0},a_{2},…,a_{n-1};0;b_{0},b_{1},…,b_{n-1})) where the non-zero diagonals are the entries of an oscillatory sequence

Subdivision of the spectra for factorable matrices on cc and ellpell ^{p}

There are many different ways to subdivide the spectrum of a bounded linear operator; some of them are motivated by applications to physics (in particular, quantum mechanics). In a series of papers, B.E. Rhoades and M. Yildirim previously investigated the spectra and fine spectra for factorable matrices, considered as bounded operators over various sequence spaces. In the present paper, approximation point spectrum, defect spectrum and compression spectrum of factorable matrices are investigated

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

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