Subdivisions of the spectra for D(r,0,s,0,t) operator on certain sequence spaces

In this paper we have examined the approximate point spectrum, defect spectrum and compression spectrum of the operator D(r,0,s,0,t) on the sequence spaces c0, c, and $bv_p (1<p<\infty)$.

On new strong versions of Browder type theorems

An operator T acting on a Banach space X satisfies the property (UWΠ) if σa(T)∖ $\begin{array}{} \sigma_{SF_{+}^{-}} \end{array} $(T) = Π(T), where σa(T) is the approximate point spectrum of T, $\begin{array}{} \sigma_{SF_{+}^{-}} \end{array} $(T) is the upper semi-Weyl spectrum of T and Π(T) the set of all poles of T. In this paper we introduce and study two new spectral properties, namely (VΠ) and (VΠa), in connection with Browder type theorems introduced in [1], [2], [3] and [4]. Among other results, we have that T satisfies property (VΠ) if and only if T satisfies property (UWΠ) and σ(T) = σa(T).

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

In this article we have determined the spectrum and fine spectrum of the Zweier matrix Z_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 Z_s on the sequence space cs.

Subdivisions of the Spectra for the Operator D(r, 0, 0, s) over Certain Sequence Spaces

In this paper we have examined the approximate point spectrum, defect spectrum and compression spectrum of the operator D(r, 0, 0, s)on the sequence spaces c0, c, ℓp and bvp.

On the fine spectrum of generalized upper triangular triple-band matrices (Δ2uvw)t over the sequence space l1

In this work, we determine the fine spectrum of the matrix operator (?2uvw)t which is defined generalized upper triangular triple band matrix on l1. Also, we give the approximate point spectrum, defect spectrum and compression spectrum of the matrix operator (?2uvw)t on l1.

Stability of essential approximate point spectrum and essential defect spectrum of linear operator

In the present paper, we use the notion of measure of noncompactness to give some results on Fredholm operators and we establish a fine description of the essential approximate point spectrum and the essential defect spectrum of a closed densely defined linear operator.

PROPERTY (Bgw) AND PERTURBATIONS

A Banach space operator T satisfies property (Bgw) if the complement in the approximate point spectrum σa(T) of the semi-B-essential approximate point spectrum σSHF+-(T) coincides with the set of isolated eigenvalues of T of Unite multiplicity E°(T). We find conditions for Banach Space operator tosatfafy the property (Bgw). We also study the stability of property (Bgw) under perturbations by nilpotent operators, by finite rank operators, by quasi-nilpotent operators and by Riesz operators commuting with T.

Weyl’s theorem for algebraically quasi-paranormal operators

Let T or T? be an algebraically quasi-paranormal operator acting on Hilbert space. We prove : (i) Weyl?s theorem holds for f (T) for every f ? H(?(T)); (ii) a-Browder?s theorem holds for f (S) for every S ? T and f ? H(?(S)); (iii) the spectral mapping theorem holds for the Weyl spectrum of T and for the essential approximate point spectrum of T.