A note on operator convergence for semigroups
A note on -hyponormal operators.
A note on preservation of spectra for two given operators
We study the relationships between the spectra derived from Fredholm theory corresponding to two given bounded linear operators acting on the same space. The main goal of this paper is to obtain sufficient conditions for which the spectra derived from Fredholm theory and other parts of the spectra corresponding to two given operators are preserved. As an application of our results, we give conditions for which the above mentioned spectra corresponding to two multiplication operators acting on the...
A note on semicharacters
A note on singular and degenerate abstract equations
Si considera l’equazione astratta , dove
A note on spectra of weighted composition operators on weighted Banach spaces of holomorphic functions.
A note on strictly cyclic shifts on .
A note on Tauberian operators.
A note on the -Browder’s and -Weyl’s theorems
Let be a Banach space operator. In this paper we characterize -Browder’s theorem for by the localized single valued extension property. Also, we characterize -Weyl’s theorem under the condition where is the set of all eigenvalues of which are isolated in the approximate point spectrum and is the set of all left poles of Some applications are also given.
A Note on the Alexander Theorem on the Complex Plane
We investigate the Banach manifold consisting of complex functions on the unit disc having boundary values in a given one-dimensional submanifold of the plane. We show that ∂/∂λ̅ restricted to that submanifold is a Fredholm mapping. Moreover, for any such function we obtain a relation between its homotopy class and the Fredholm index.
A note on the almost everywhere convergence of alternating sequences with Dunford-Schwartz operators
A note on the almost left and almost right joint spectra of R. Harte
A note on the asymptotics of perturbed expanding maps.
A note on the differentiable structure of generalized idempotents
For a fixed n > 2, we study the set Λ of generalized idempotents, which are operators satisfying T n+1 = T. Also the subsets Λ†, of operators such that T n−1 is the Moore-Penrose pseudo-inverse of T, and Λ*, of operators such that T n−1 = T* (known as generalized projections) are studied. The local smooth structure of these sets is examined.
A note on the hyperreflexivity constant for certain reflexive algebras
Using results on the reflexive algebra with two invariant subspaces, we calculate the hyperreflexivity constant for this algebra when the Hilbert space is two-dimensional. Then by the continuity of the angle for two subspaces, there exists a non-CSL hyperreflexive algebra with hyperreflexivity constant C for every C>1. This result leads to a kind of continuity for the hyperreflexivity constant.
A note on the index of -Fredholm operators
From Corollary 3.5 in [Berkani, M; Sarih, M.; Studia Math. 148 (2001), 251–257] we know that if , are commuting -Fredholm operators acting on a Banach space , then is a -Fredholm operator. In this note we show that in general we do not have , contrarily to what has been announced in Theorem 3.2 in [Berkani, M; Proc. Amer. Math. Soc. 130 (2002), 1717–1723]. However, if there exist such that , , , are commuting and , then , where stands for the index of a -Fredholm operator.
A note on the integral criterion for spectral dichotomy of regular pencils.
A note on the minimax principle for -positive operators
A note on the powers of Cesàro bounded operators
In this note we give a negative answer to Zem�nek’s question (1994) of whether it always holds that a Cesàro bounded operator on a Hilbert space with a single spectrum satisfies
A note on the range of the operator defined on .