We study the set X of split operators acting in the Hilbert space H: X = {T ∈ B(H) : N(T) ∩ R(T) = {0} and N(T) + R(T) = H}. Inside X , we consider the set Y: Y = {T ∈ X : N(T) ⊥ R(T)}. Several characterizations of these ...

Given a Krein space H and B, C in L(H), L(H), the bounded linear operators on H, the minimization/maximization of expressions of the form (BX−C)#(BX−C) as X runs over L(H) is studied. Complete solutions are found for the ...

Let CR be the set of all bounded linear operators between Hilbert spaces H, K with closed range. This paper is devoted to the study of the topological properties of CR if certain natural metrics are considered on it. We ...

An innovative numerical method based on an artificial neural network is presented in order to solve an inverse problem associated with the calculation of the Dirichlet eigenvalues of the anisotropic Laplace operator. Using ...

In this paper, left and right generalized Drazin invertible operators on Banach spaces are defined and characterized by means of the generalized Kato decomposition. Then, new binary relations associated with these operators ...

In this article we deal with a class of geometric inverse problem for bottom detection by one single measurement on the free surface in water-waves. We found upper and lower bounds for the size of the region enclosed between ...