Automatic continuity of linear maps on spaces of continuous functions.
Automatic continuity of operational calculi on algebras of differentiable functions
Automatic continuity of operators commuting with translations
Let and be representations of a topological group G on Banach spaces X and Y, respectively. We investigate the continuity of the linear operators Φ: X → Y with the property that for each t ∈ G in terms of the invariant vectors in Y and the automatic continuity of the invariant linear functionals on X.
Automatic Continuity over Moore Groups.
Automatische Stetigkeitseigenschaften einiger Klassen linearer Operatoren.
Automorphic forms, hyperfunction cohomology, and period functions.
Automorphism Groups of Jordan C*-Algebras.
Automorphismes et dérivations de «petites normes» sur un corps value non archimédien
Automorphisms and derivations of a Fréchet algebra of locally integrable functions
We find representations for the automorphisms, derivations and multipliers of the Fréchet algebra of locally integrable functions on the half-line . We show, among other things, that every automorphism θ of is of the form , where D is a derivation, X is the operator of multiplication by coordinate, λ is a complex number, a > 0, and is the dilation operator (, ). It is also shown that the automorphism group is a topological group with the topology of uniform convergence on bounded...
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 central extensions of type I von Neumann algebras
Given a von Neumann algebra M we consider its central extension E(M). For type I von Neumann algebras, E(M) coincides with the algebra LS(M) of all locally measurable operators affiliated with M. In this case we show that an arbitrary automorphism T of E(M) can be decomposed as , where is an inner automorphism implemented by an element a ∈ E(M), and is a special automorphism generated by an automorphism ϕ of the center of E(M). In particular if M is of type then every band preserving automorphism...
Automorphisms of Inductive Limit C*-Algebras.
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 on the spaces of entire functions of several variables over non-archimedean fields.
*-autonomous categories: Once more around the track.
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 uniformly continuous retractions
Let X be an infinite-dimensional complex normed space, and let B and S be its closed unit ball and unit sphere, respectively. We prove that the identity map on B can be expressed as an average of three uniformly retractions of B onto S. Moreover, for every 0≤ r < 1, the three retractions are Lipschitz on rB. We also show that a stronger version where the retractions are required to be Lipschitz does not hold.
Averaging at any level.
Axiomatic analyticity properties and representations of particles in thermal quantum field theory