Abstract In this paper we are concerned with the spectral analysis for the classes of finte rank perturbations of diagonal operators in the form A = D+F where D is a diagonal operator and F = u’1 ⊗v’1+...+u’m ⊗vm is an operator of finite rank in the non-archimedean Banach space of countable type. We compute the spectrum of A using the theory of Fredholm operators in non archimedean setting and the concept of essential spectrum for linear operators.

Abstract We study common local spectral properties for bounded linear operators A ∈ ℒ(X,Y) and B,C ∈ ℒ (Y,X) such that A(BA) 2 =ABACA=ACABA=(AC) 2 A. We prove that AC and BA share the single valued extension property, the Bishop property (β), the property (β ε ), the decomposition property (δ) and decomposability. Closedness of analytic core and quasinilpotent part are also investigated. Some applications to Fredholm operators are given.

We will present sufficient conditions for the Fredholm property of Wiener-Hopf plus and minus Hankel operators with different Fourier matrix symbols in the C*-algebra of semialmost periodic elements. In addition, under such conditions, we will derive a formula for the sum of the Fredholm indices of theseWiener-Hopf plus Hankel and Wiener-Hopf minus Hankel operators. Some examples are provided to illustrate the results of the paper.

Presentaremos condiciones suficientes para garantizar la propiedad de Fredholm de operadores de tipo Wiener-Hopf más y menos Hankel con diferentes símbolos de Fourier matriciales en la C*-álgebra de elementos semi-casi periódicos. Además, bajo tales condiciones, obtendremos una fórmula para la suma de los ´ındices de Fredholm de estos operadores Wiener-Hopf más Hankel y Wiener-Hopf menos Hankel. Algunos ejemplos son dados para ilustrar los resultados del artículo.