A new proof of the monotonicity of the Temple quotients for the computation of the dominant eigenvalue of a bounded linear normal operator in a Hilbert space is given. Another goal of the paper is a precise analysis of the length of the interval for admissible shifts for the Temple quotients.
We consider Schrödinger operators with dynamically defined potentials arising from continuous sampling along orbits of strictly ergodic transformations. The Gap Labeling Theorem states that the possible gaps in the spectrum can be canonically labelled by an at most countable set defined purely in terms of the dynamics. Which labels actually appear depends on the choice of the sampling function; the missing labels are said to correspond to collapsed gaps. Here we show that for any collapsed gap,...
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...
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.
Several operational quantities have appeared in the literature characterizing upper semi-Fredholm operators. Here we show that these quantities can be divided into three classes, in such a way that two of them are equivalent if they belong to the same class, and are comparable and not equivalent if they belong to different classes. Moreover, we give a similar classification for operational quantities characterizing lower semi-Fredholm operators.
Several operational quantities, defined in terms of the norm and the class of finite dimensional Banach spaces, have been used to characterize the classes of upper and lower semi-Fredholm operators, strictly singular and strictly cosingular operators, and to derive some perturbation results.In this paper we shall introduce and study some operational quantities derived from the norm and associated to a space ideal. By means of these quantities we construct a generalized Fredholm theory in which...
We introduce and study some operational quantities associated to a space ideal . These quantities are used to define generalized semi-Fredholm operators associated to , and the corresponding perturbation classes which extend the strictly singular and strictly cosingular operators, and we study the generalized Fredholm theory obtained in this way. Finally we present some examples and show that the classes of generalized semi-Fredholm operators are non-trivial for several classical space ideals.