Elementary operators and subhomogeneous -algebras. II.
Elementary operators on Banach algebras and Fourier transform
We consider elementary operators , acting on a unital Banach algebra, where and are separately commuting families of generalized scalar elements. We give an ascent estimate and a lower bound estimate for such an operator. Additionally, we give a weak variant of the Fuglede-Putnam theorem for an elementary operator with strongly commuting families and , i.e. (), where all and ( and ) commute. The main tool is an L¹ estimate of the Fourier transform of a certain class of functions...
Elementary operators on prome C*-algebras. I.
Elementary Tauberian Theorems For Regular Linear Operators
Elementary Tauberian theorems for regular linear operators.
Elements of C*-algebras commuting with their Moore-Penrose inverse
We give new necessary and sufficient conditions for an element of a C*-algebra to commute with its Moore-Penrose inverse. We then study conditions which ensure that this property is preserved under multiplication. As a special case of our results we recover a recent theorem of Hartwig and Katz on EP matrices.
Elliptic and degenerate-elliptic operators in unbounded domains
Elliptic Boundary Problems and the Boutet de Monvel Calculus in Besov and Triebel-Lizorkin Spaces.
Elliptic corner operators in spaces with continuous radial asymptotics II
Asymptotic expansions at the origin with respect to the radial variable are established for solutions to equations with smooth 2-dimensional singular Fuchsian type operators.
Elliptic Equations with Noninvertible Fredholm Linear Part and Bounded Nonlinearities.
Elliptic perturbations for Hammerstein equations with singular nonlinear term.
Elliptic regularity and essential self-adjointness of Dirichlet operators on
Elliptic resonance problems with unequal limits at infinity.
Elliptic Systems of Pseudodifferential Equations in the Refined Scale on a Closed Manifold
We study a system of pseudodifferential equations which is elliptic in the Petrovskii sense on a closed smooth manifold. We prove that the operator generated by the system is a Fredholm operator in a refined two-sided scale of Hilbert function spaces. Elements of this scale are special isotropic spaces of Hörmander-Volevich-Paneah.
Embedded eigenvalues and resonances of Schrödinger operators with two channels
In this article, we give a necessary and sufficient condition in the perturbation regime on the existence of eigenvalues embedded between two thresholds. For an eigenvalue of the unperturbed operator embedded at a threshold, we prove that it can produce both discrete eigenvalues and resonances. The locations of the eigenvalues and resonances are given.
Embedding C(K) in B(X).
Embedding theorems for Müntz spaces
We discuss boundedness and compactness properties of the embedding , where is the closed linear span of the monomials in and is a finite positive Borel measure on the interval . In particular, we introduce a class of “sublinear” measures and provide a rather complete solution of the embedding problem for the class of quasilacunary sequences . Finally, we show how one can recapture some of Al Alam’s results on boundedness and the essential norm of weighted composition operators from ...
Embeddings of finite-dimensional operator spaces into the second dual
We show that, if a a finite-dimensional operator space E is such that X contains E C-completely isomorphically whenever X** contains E completely isometrically, then E is -completely isomorphic to Rₘ ⊕ Cₙ for some n, m ∈ ℕ ∪ 0. The converse is also true: if X** contains Rₘ ⊕ Cₙ λ-completely isomorphically, then X contains Rₘ ⊕ Cₙ (2λ + ε)-completely isomorphically for any ε > 0.
Embeddings of Sobolev spaces
Empathy theory and the Laplace transform
This paper is concerned with double families of evolution operators employed in the study of dynamical systems in which cause and effect are represented in different Banach spaces. The main tool is the Laplace transform of vector-valued functions. It is used to define the generator of the double family which is a pair of unbounded linear operators and relates to implicit evolution equations in a direct manner. The characterization of generators for a special class of evolutions is presented.