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 commutator of two operators on a locally convex space
Denote by the commutator of two bounded operators and acting on a locally convex topological vector space. If , we show that is a quasinilpotent operator and we prove that if is a compact operator, then is a Riesz operator.
A note on the comparison of C0-semigroups.
A note on the continuity properties of nonlinear operators
A note on the convolution theorem for the Fourier transform
In this paper we characterize those bounded linear transformations carrying into the space of bounded continuous functions on , for which the convolution identity holds. It is shown that such a transformation is just the Fourier transform combined with an appropriate change of variable.
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 example of J. Andres concerning the application of the Nielsen fixed-point theory to differential systems
A note on the existence of more than one solution for asymptotically linear equations
A note on the existence of solutions to some nonlinear functional integral equations.
A note on the growth bound of Co-semigroups.
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 Measure of Solvability
Let X be an infinite-dimensional Banach space. The measure of solvability ν(I) of the identity operator I is equal to 1.
A note on the minimal essential set of coincident points for set-valued mappings.
A note on the minimax principle for -positive operators
A Note on the Paper "Hermitian Operators on C(X, E) and Banach-Stone Theorem" by R.J. Fleming and J.E.Jamison.
A note on the paper of Shütt "Unconditionality in tensor products''