On the fine spectra of triangular Toeplitz operators

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

“…Altay and Karakuş [24] determined the fine spectrum of the Zweier matrix which is a band matrix as an operator over the sequence spaces ℓ 1 and V. In 2010, Srivastava and Kumar [16] determined the spectra and the fine spectra of the double sequential band matrix Δ ] on ℓ 1 , where Δ ] is defined by (Δ ] ) = ] and (Δ ] ) +1, = −] for all ∈ N, under certain conditions on the sequence ] = (] ) and they have just generalized these results by the double sequential band matrix Δ V defined by Δ V = ( + V −1 −1 ) ∈N for all ∈ N (see [18]). 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].…”

Spectrum and fine spectrum of generalized lower triangular triple band matrices over the sequence space lp

“…Furkan et al [7,8], Bilgiç and Furkan [9] further generalised these results to the operator B(r, s, t). The fine spectrum of triangular Toeplitz operator defined on c 0 and c is obtained by Altun [10]. Srivastava and Kumar [11,12] have studied the spectrum and fine spectrm of the generalised differnece operators △ v and △ uv on l 1 .…”

Fine spectrum of the upper triangular matrix U(𝒓,0,0,𝒔) over the sequence spaces 𝒄₀ and 𝒄

“…Altay and Başar [3,4] determined the fine spectrum of the difference operator ∆ and the generalized difference operator B(r, s) on the sequence spaces c 0 and c. The spectrum and fine spectrum of the Zweier Matrix on the sequence spaces 1 and bv were studied by Altay and Karakuş [5]. Altun [6,7] determined the fine spectra of triangular Toeplitz operators and tridiagonal symmetric matrices over some sequence spaces. Fine spectra of operator B(r, s, t) over the sequence spaces 1 and bv and generalized difference operator B(r, s) over the sequence spaces p and bv p , (1 ≤ p < ∞) were studied by Bilgiç and Furkan [9,10].…”