On the computation of some quantities in the theory of Fredholm operators
On the essential approximate point spectrum II
On the essential spectra of matrix operators and applications.
On the existence of solution of the equation and a generalized coincidence degree theory. II.
On the generalized boundary value problem
In the paper it is proved that the generalized linear boundary value problem generates a Fredholm operator. Its index depends on the number of boundary conditions. The existence results of Landesman-Lazer type are given as an application to nonlinear problems by using dual generalized boundary value problems.
On the Index of Callias-type Operators.
On the Index of Toeplitz Operators of Several Complex Variables.
On the isomorphism of cartesian products of locally convex spaces
On the Multiplicity of an Analytic Operator-Valued Function.
On the Neumann operator of the arithmetical mean.
On the norm-closure of the class of hypercyclic operators
Let T be a bounded linear operator acting on a complex, separable, infinite-dimensional Hilbert space and let f: D → ℂ be an analytic function defined on an open set D ⊆ ℂ which contains the spectrum of T. If T is the limit of hypercyclic operators and if f is nonconstant on every connected component of D, then f(T) is the limit of hypercyclic operators if and only if is connected, where denotes the Weyl spectrum of T.
On the perturbation functions and similarity orbits
We show that the essential spectral radius of T ∈ B(H) can be calculated by the formula = inf: X an invertible operator, where is a Φ₁-perturbation function introduced by Mbekhta [J. Operator Theory 51 (2004)]. Also, we show that if is a Φ₂-perturbation function [loc. cit.] and if T is a Fredholm operator, then = sup: X an invertible operator.
On the semi-Browder spectrum
An operator in a Banach space is called upper (lower) semi-Browder if it is upper (lower) semi-Fredholm and has a finite ascent (descent). We extend this notion to n-tuples of commuting operators and show that this notion defines a joint spectrum. Further we study relations between semi-Browder and (essentially) semiregular operators.
On the solutions of nonlinear initial-boundary value problems.
On the Spectra of Finite-Dimensional Pertobations of Matrix Multiplication Operators.
On the spectral properties of tensor products of linear operators in Banach spaces
On uniqueness in electromagnetic scattering from biperiodic structures
Consider time-harmonic electromagnetic wave scattering from a biperiodic dielectric structure mounted on a perfectly conducting plate in three dimensions. Given that uniqueness of solution holds, existence of solution follows from a well-known Fredholm framework for the variational formulation of the problem in a suitable Sobolev space. In this paper, we derive a Rellich identity for a solution to this variational problem under suitable smoothness conditions on the material parameter. Under additional...
Opérateurs de Riesz dont le coeur analytique est fermé
Dans ce travail nous donnons plusieurs caractérisations, en termes spectraux, d'opérateurs de Riesz dont le coeur analytique est fermé. Notamment, nous montrons que pour un opérateur de Riesz T, le coeur analytique est fermé si et seulement si sa dimension est finie si et seulement si zéro est isolé dans le spectre de T si et seulement si T = Q + F avec QF = FQ = 0, F de rang fini et Q quasinilpotent. Ce dernier résultat montre qu'un opérateur de Riesz dont le coeur analytique est fermé admet la...
Operational quantities.
Operational quantities
In this paper we consider maps called operational quantities, which assign a non-negative real number to every operator acting between Banach spaces, and we obtain relations between the kernels of these operational quantities and the classes of operators of the Fredholm theory.