Search results for "Operator"
showing 10 items of 1427 documents
Compact and Weakly Compact Homomorphisms on Fréchet Algebras of Holomorphic Functions
2002
We study homomorphisms between Frechet algebras of holomorphic functions of bounded type. In this setting we prove that any pointwise bounded homomorphism into the space of entire functions of bounded type is rank one. We characterize up to the approximation property of the underlying Banach space, the weakly compact composition operators on Hb(V), V absolutely convex open set.
Quantum extensions of semigroups generated by Bessel processes
1996
We construct a quantum extension of the Markov semigroup of the classical Bessel process of orderv≥1 to the noncommutative von Neumann algebra s(L2(0, +∞)) of bounded operators onL2(0, +∞).
On certain linear operators in spaces of ultradifferentiable functions
1996
Let ω be a weight in the sense of Braun, Meise, Taylor, which defines a non-quasianalytic class. Let H be a compact subset of ℝn. It is proved that for every function ƒ on ℝn which belongs to the non-quasianalytic (ω)-class, there is an element g of the same class which is analytic on ℝn\H and such that Dαƒ(x) = Dαg(x) for every x ∈ H and α ∈ ℕ0n. A similar result is proved for functions of the Roumieu type. Continuous linear extension operators of Whitney jets with additional properties are also obtained.
The Fine Spectre of Some Cesàro Generalized Operators Defined onℓp(p> 1)
2004
Abstract The aim of the paper is the study of the fine spectre for a class of Cesaro generalized operators, Rhaly operators, when those operators are defined on the spaces lp, p > 1.
Composition operators on uniform algebras, essential norms, and hyperbolically bounded sets
2006
Let A be a uniform algebra, and let o be a self-map of the spectrum M A of A that induces a composition operator C o on A. The object of this paper is to relate the notion of "hyperbolic boundedness" introduced by the authors in 2004 to the essential spectrum of C o . It is shown that the essential spectral radius of C o , is strictly less than 1 if and only if the image of M A under some iterate o n of o is hyperbolically bounded. The set of composition operators is partitioned into "hyperbolic vicinities" that are clopen with respect to the essential operator norm. This partition is related to the analogous partition with respect to the uniform operator norm.
Multiplicative Decompositions of Holomorphic Fredholm Functions and ψ*-Algebras
1999
In this article we construct multiplicative decompositions of holomorphic Fredholm operator valued functions on Stein manifolds with values in various algebras of differential and pseudo differential operators which are submultiplicative ψ* - algebras, a concept introduced by the first author. For Fredholm functions T(z) satisfying an obvious topological condition we. Prove (0.1) T(z) = A(z)(I + S(z)), where A(z) is holomorphic and invertible and S(z) is holomorphic with values in an “arbitrarily small” operator ideal. This is a stronger condition on S(z) than in the authors' additive decomposition theorem for meromorphic inverses of holomorphic Fredholm functions [12], where the smallness …
Singular Perturbations and Operators in Rigged Hilbert Spaces
2015
A notion of regularity and singularity for a special class of operators acting in a rigged Hilbert space \({\mathcal{D} \subset \mathcal{H}\subset \mathcal{D}^\times}\) is proposed and it is shown that each operator decomposes into a sum of a regular and a singular part. This property is strictly related to the corresponding notion for sesquilinear forms. A particular attention is devoted to those operators that are neither regular nor singular, pointing out that a part of them can be seen as perturbation of a self-adjoint operator on \({\mathcal{H}}\). Some properties for such operators are derived and some examples are discussed.
On the regularity of the partial {$O\sp *$}-algebras generated by a closed symmetric operator
1992
Let be given a dense domain D in a Hilbert space and a closed symmetric operator T with domain containing D. Then the restriction of T to D generates (algebraically) two partial *-algebras of closable operators (called weak and strong), possibly nonabelian and nonassociative. We characterize them completely. In particular, we examine under what conditions they are regular, that is, consist of polynomials only, and standard. Simple differential operators provide concrete examples of all the pathologies allowed by the abstract theory.
Automatic continuity of generalized local linear operators
1980
In this note, we present a general automatic continuity theory for linear mappings between certain topological vector spaces. The theory applies, in particular, to local operators between spaces of functions and distributions, to algebraic homomorphisms between certain topological algebras, and to linear mappings intertwining generalized scalar operators.
On spectra of geometric operators on open manifolds and differentiable groupoids
2001
We use a pseudodifferential calculus on differentiable groupoids to obtain new analytical results on geometric operators on certain noncompact Riemannian manifolds. The first step is to establish that the geometric operators belong to a pseudodifferential calculus on an associated differentiable groupoid. This then leads to Fredholmness criteria for geometric operators on suitable noncompact manifolds, as well as to an inductive procedure to compute their essential spectra. As an application, we answer a question of Melrose on the essential spectrum of the Laplace operator on manifolds with multicylindrical ends.