On Property (Saw) and others spectral properties type Weyl-Browder theorems

Abstract

Revista Colombiana de MatemáticasVolumen 51(2017)2, páginas 153-171On Property (Saw) and others spectral properties type Weyl-Browder theorems Abstract. An operator T acting on a Banach space X satisfies the property, where σW (T ) is the Weyl spectrum of T and E 0 a (T ) is the set of all eigenvalues of T of finite multiplicity that are isolated in the approximate point spectrum of T . In this paper we introduce and study two new spectral properties, namely (Saw) and (Sab), in connection with Weyl-Browder type theorems. Among other results, we prove that T satisfies property (Saw) if and only if T satisfies property (aw) and σ SBF Resumen. Un operador T actuando sobre un espacio de Banach X satisface la propiedad (aw) si σ(T ) \ σW (T ) = E 0 a (T ), donde σW (T ) es el espectro de Weyl de T y E 0 a (T ) es el conjunto de todos los autovalores de T de multiplicidad finita que son aislados en el espectro aproximado puntual de T . En este artículo introducimos y estudiamos dos nuevas propiedades espectrales, llamadas (Saw) y (Sab), en conexión con teoremas tipo Weyl-Browder. Entre

Weyl's theorem and property (Saw)

“…An operator T is said to have SVEP, if T has SVEP at every point λ ∈ C. Aiena has proved the following result for operators whose adjoints have SVEP. In this sequence, Sanabria [8] has shown that property(Saw) ⇒ Weyl's theorem…”

Perturbation Theory for Property (VE) and Tensor Product

“…For T ∈ L(X ), let T * , T (X ) and N(T ) be the dual operator, the range and the kernel of T , respectively. We will use the following spectra of T : [17,18] for definitions and other details.…”

Further characterizations of property (VΠ) and some applications

“…Further characterizations of property (V Π ) and some applications 1455 [18], we say that T verifies property (Sab) if σ(T ) \ σ ubw (T ) = p a 00 (T ). In [18,Corollary 2.9], it is shown that property (Sab) is equivalent to property (Sb). Recall [20] that an operator T ∈ L(X) verifies property (V Πa ) if σ(T ) \ σ uw (T ) = Π a (T ).…”

“…Property (V Π ) is a strong variant of classical Browder's theorem and their generalized versions, which was recently introduced by Sanabria et al [20]. There are other strong versions of Browder's theorem that are equivalent to property (V Π ), such is the case of properties (Sb), (Sab), and (V Π a ) introduced in [17], [18] and [20], respectively. In this paper we investigated new characterizations of property (V Π ) using the localized single-valued extension property and some topological conditions that satisfy the spectral subsets originated from Fredholm Theory and B-Fredholm Theory.…”