Fine spectra of upper triangular double-band matrices

Abstract

a b s t r a c tThe fine spectra of lower triangular double-band matrices have been examined by several authors (e.g. [13,22]). Here we determine the fine spectra of upper triangular double-band matrices over the sequence spaces c 0 and c. Upper triangular double-band matrices are infinite matrices which include the left-shift, averaging and difference operators.

On the fine spectra of triangular Toeplitz operators

“…If we take PðzÞ ¼ r þ sz, then the corresponding lower triangular Toeplitz operator is the Bðr; sÞ of [1] and the corresponding upper triangular Toeplitz operator is the Uðr; sÞ of [10], so our results include the corresponding results given in [1] and [10]. If we take PðzÞ ¼ r þ sz þ tz 2 , then the corresponding lower triangular Toeplitz operator is the Bðr; s; tÞ of [5] and our results also include the corresponding results given in [5].…”

“…In this paper, we determine the spectrum, the point spectrum, the continuous spectrum and the residual spectrum of the operators T ½L ðaÞ and T ½U ðaÞ over the sequence spaces c 0 and c. The paper gives results for a wide range of new operators, and also includes the corresponding results of [1,5,10].…”

On the Fine Spectrum of the Operator Defined by the Lambda Matrix over the Spaces of Null and Convergent Sequences

“…Altun [25] studied the fine spectra of the Toeplitz operators, which are represented by upper and lower triangular -band infinite matrices, over the sequence spaces 0 and . Later, Karakaya and Altun determined the fine spectra of upper triangular double-band matrices over the sequence spaces 0 and , in [26]. Quite recently, Akhmedov and El-Shabrawy [15] obtained the fine spectrum of the double sequential band matrix Δ , , defined as a doubleband matrix with the convergent sequences̃= ( ) and̃= ( ) having certain properties, over the sequence space .…”

Spectrum and fine spectrum of the Zweier matrix over the sequence space cs

“…Panigrahi and Srivastava [24,25] studied the spectrum and fine spectrum of the second order difference operator ∆ 2 uv on the sequence space c 0 and generalized second order forward difference operator ∆ 2 uvw on the sequence space ℓ 1 . Fine spectra of upper triangular double-band matrix U (r, s) over the sequence spaces c 0 and c were studied by Karakaya and Altun [20]. Karaisa and Başar [19] have determined the spectrum and fine spectrum of the upper traiangular matrix A(r, s, t) over the sequence space ℓ p , (0 < p < ∞).…”