A bounded operator T ∈ L(X), X a Banach space, is said to verify generalized Browder's theorem if the set of all spectral points that do not belong to the B-Weyl's spectrum coincides with the set of all poles of the resolvent of T , while T is said to verify generalized Weyl's theorem if the set of all spectral points that do not belong to the B-Weyl spectrum coincides with the set of all isolated points of the spectrum which are eigenvalues. In this article we characterize the bounded linear operators T satisfying generalized Browder's theorem, or generalized Weyl's theorem, by means of localized SVEP, as well as by means of the quasi-nilpotent part H0(λI −T ) as λ belongs to certain subsets of C. In the last part we give a general framework for which generalized Weyl's theorem follows for several classes of operators. Mathematics Subject Classification (2000). Primary 47A10, 47A11; Secondary 47A53, 47A55.

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).

In this paper we study the relationships between the B-Browder spectra and some other spectra originating from Fredholm theory and BFredholm theory. This study is done by using the localized single valued extension property. In particular, we shall see that many spectra coincide in the case that a bounded operator T , or its dual T * , or both, admits the single valued extension property.

The complex [Cu(en) 2 (H 2 O)](sy) 2 (en)(H 2 O) 2 has been synthesized and characterized by its electronic and vibrational spectra. The molecular structure of the complex has been determined by X-ray diffraction methods. The complex crystallizes in the orthorhombic space group Pnma with unit-cell parameters a = 10.7236 (5), b = 20.4660(10), c = 14.4523(11)Å and Z = 4. In the cation, the Cu(II) ion has a distorted square pyramidal coordination with two bidendate (en) ligands forming the basal plane and a H 2 O molecule in the apical position. The complex cations and syringate anions constitute chains along the b axis in -A-B-A-fashion. The members of the chains are linked by through N-H···O hydrogen bonds. The (en) molecules are responsible for connecting adjacent layers.

In this paper, we study the stability under direct sums and restrictions of some strong variations of Weyl and Browder type theorems recently introduced in Rashid and Prasad (