Aufspaltungen linearer gewöhnlicher Differentialoperatoren und der zugehörigen Greenschen Funktion.
Automatic continuity of biseparating maps
We prove that a biseparating map between spaces of vector-valued continuous functions is usually automatically continuous. However, we also discuss special cases when this is not true.
Automatic continuity of linear maps on spaces of continuous functions.
Automatic continuity of operational calculi on algebras of differentiable functions
Automatic continuity of translation - invariant linear operators
Automatic extensions of functional calculi
Given a Banach algebra ℱ of complex-valued functions and a closed, linear (possibly unbounded) densely defined operator A, on a Banach space, with an ℱ functional calculus we present two ways of extending this functional calculus to a much larger class of functions with little or no growth conditions. We apply this to spectral operators of scalar type, generators of bounded strongly continuous groups and operators whose resolvent set contains a half-line. For f in this larger class, one construction...
Automorphismes et dérivations de «petites normes» sur un corps value non archimédien
Automorphisms and derivations on a universally complete complex -algebra.
Automorphisms of C commuting with partial integration operators in a rectangle
Convolutional representations of the commutant of the partial integration operators in the space of continuous functions in a rectangle are found. Necessary and sufficient conditions are obtained for two types of representing functions, to be the operators in the commutant continuous automorphisms. It is shown that these conditions are equivalent to the requirement that the considered representing functions be joint cyclic elements of the partial integration operators.
Automorphisms of linear semigroups over division rings.
Automorphisms of the algebra of operators in preserving conditioning
Let α be an isometric automorphism of the algebra of bounded linear operators in (p ≥ 1). Then α transforms conditional expectations into conditional expectations if and only if α is induced by a measure preserving isomorphism of [0, 1].
Automorphisms of the Loeb algebra
Auxiliary principle for generalized nonlinear variational-like inequalities.
Auxiliary principle for generalized strongly nonlinear mixed variational-like inequalities.
Averages of holomorphic mappings and holomorphic retractions on convex hyperbolic domains
Let D be a hyperbolic convex domain in a complex Banach space. Let the mapping F ∈ Hol(D,D) be bounded on each subset strictly inside D, and have a nonempty fixed point set ℱ in D. We consider several methods for constructing retractions onto ℱ under local assumptions of ergodic type. Furthermore, we study the asymptotic behavior of the Cesàro averages of one-parameter semigroups generated by holomorphic mappings.
Averages of unitary representations and weak mixing of random walks
Let S be a locally compact (σ-compact) group or semigroup, and let T(t) be a continuous representation of S by contractions in a Banach space X. For a regular probability μ on S, we study the convergence of the powers of the μ-average Ux = ʃ T(t)xdμ(t). Our main results for random walks on a group G are: (i) The following are equivalent for an adapted regular probability on G: μ is strictly aperiodic; converges weakly for every continuous unitary representation of G; U is weakly mixing for any...
Averaging in an ordinary differential equation.
Averaging theorems for linear operators in compact groups and semigroups
The Weyl criterion for uniform distribution of a sequence has an especially simple form in compact abelian groups. The authors use this and the structure of compact monothetic groups and semigroups to generalise the convergence, under certain compactness conditions, of the operator averages: where P is a projection associated with the eigenvalue one of T.
a-Weyl's theorem and perturbations
We study the stability of a-Weyl's theorem under perturbations by operators in some known classes. We establish in particular that if T is a finite a-isoloid operator, then a-Weyl's theorem is transmitted from T to T + R for every Riesz operator R commuting with T.
a-Weyl's theorem and the single valued extension property.
In the present paper, we study a-Weyl's and a-Browder's theorem for an operator T such that T or T* satisfies the single valued extension property (SVEP). We establish that if T* has the SVEP, then T obeys a-Weyl's theorem if and only if it obeys Weyl's theorem. Further, if T or T* has the SVEP, we show that the spectral mapping theorem holds for the essential approximative point spectrum, and that a-Browder's theorem is satisfied by f(T) whenever f ∈ H(σ(T)). We also provide several conditions...