On the Banach principle.
On the Closedness of the Sum of Two Closed Operators.
On the commutativity of two projections.
On the convergence and unconditional convergence of series of operators on Banach spaces.
We study Kalton's theorem on the unconditional convergence of series of compact operators and we use some matrix techniques to obtain sufficient conditions, weaker than the previous one, on the convergence and unconditional convergence of series of compact operators.
On the convergence of Neumann series for noncompact operators
On the convergence of semiiterative methods to the Drazin inverse solution of linear equations in Banach spaces.
On the convergence of sequences of linear operators and adjoint operators
On the Existence of Minimal Operators for Schrödinger-Type Differential Expressions.
On the extension of linear operators.
On the finite dimensional orbits of linear operators
On the generalized Drazin inverse and generalized resolvent
We investigate the generalized Drazin inverse and the generalized resolvent in Banach algebras. The Laurent expansion of the generalized resolvent in Banach algebras is introduced. The Drazin index of a Banach algebra element is characterized in terms of the existence of a particularly chosen limit process. As an application, the computing of the Moore-Penrose inverse in -algebras is considered. We investigate the generalized Drazin inverse as an outer inverse with prescribed range and kernel....
On the Moore-Penrose inverse in C*-algebras.
In this article, two results regarding the Moore-Penrose inverse in the frame of C*-algebras are considered. In first place, a characterization of the so-called reverse order law is given, which provides a solution of a problem posed by M. Mbekhta. On the other hand, Moore-Penrose hermitian elements, that is C*-algebra elements which coincide with their Moore-Penrose inverse, are introduced and studied. In fact, these elements will be fully characterized both in the Hilbert space and in the C*-algebra...
On the Normality of the Unbounded Product of Two Normal Operators
Let A and B be two -non necessarily bounded- normal operators. We give new conditions making their product normal. We also generalize a result by Deutsch et al on normal products of matrices.
On the Putnam--Fuglede theorem.
On the range of a closed operator in an -space of vector-valued functions
Let be a reflexive Banach space and be a closed operator in an -space of -valued functions. Then we characterize the range of as follows. Let for all , where denotes the resolvent set of , and assume that and . Furthermore, assume that there exists such that . Then is equivalent to . This generalizes Shaw’s result for scalar-valued functions.
On the right inverse operators which are defined by Eidelheit sequences.
On the spectral bound of the generator of a -semigroup
We give several conditions implying that the spectral bound of the generator of a -semigroup is negative. Applications to stability theory are considered.
On Weak Convergence of Norm Preserving Operators on L2 (X) and its Application to Measure Preserving Transformations.
Operadores antisimétricos y de rango finito en espacios de Hilbert.
Operator matrix of Moore-Penrose inverse operators on Hilbert C*-modules
We show that the Moore-Penrose inverse of an operator T is idempotent if and only if it is a product of two projections. Furthermore, if P and Q are two projections, we find a relation between the entries of the associated operator matrix of PQ and the entries of associated operator matrix of the Moore-Penrose inverse of PQ in a certain orthogonal decomposition of Hilbert C*-modules.