Search results for "Holomorph"
showing 10 items of 111 documents
ISOMETRY GROUPS OF WEIGHTED SPACES OF HOLOMORPHIC FUNCTIONS: TRANSITIVITY AND UNIQUENESS
2009
We survey some recent results on the isometries of weighted spaces of holomorphic functions defined on an open subset of ℂn. We will see that these isometries are determined by a subgroup of the automorphisms on a distinguished subset of the domain. We will look for weights with 'large' groups of isometries and observe that in certain circumstances the group of isometries determines the weight.
Linearization of holomorphic mappings on fully nuclear spaces with a basis
1994
In [13] Mazet proved the following result.If U is an open subset of a locally convex space E then there exists a complete locally convex space (U) and a holomorphic mapping δU: U→(U) such that for any complete locally convex space F and any f ɛ ℋ (U;F), the space of holomorphic mappings from U to F, there exists a unique linear mapping Tf: (U)→F such that the following diagram commutes;The space (U) is unique up to a linear topological isomorphism. Previously, similar but less general constructions, have been considered by Ryan [16] and Schottenloher [17].
Weakly uniformly continuous holomorphic functions and the approximation property
2001
Abstract We study the approximation property for spaces of Frechet and Gâteaux holomorphic functions which are weakly uniformly continuous on bounded sets. We show when U is a balanced open subset of a Baire or barrelled metrizable locally convex space, E , that the space of holomorphic functions which are weakly uniformly continuous on U -bounded sets has the approximation property if and only if the strong dual of E , E ′ b , has the approximation property. We also characterise the approximation property for these spaces of vector-valued holomorphic functions in terms of the tensor product of the corresponding space of scalar-valued holomorphic functions and the range space.
The spectra of some algebras of analytic mappings
1999
Abstract Let E be a Banach space with the approximation property and let F be a Banach algebra with identity. We study the spectrum of the algebra H b(E, F) of all holomorphic mappings f : E → F that are bounded on the bounded subsets of E.
Holomorphically ultrabornological spaces and holomorphic inductive limits
1987
Abstract The holomorphically ultrabornological spaces are introduced. Their relation with other holomorphically significant classes of locally convex spaces is established and separating examples are given. Some apparently new properties of holomorphically barrelled spaces are included and holomorphically ultrabornological spaces are utilized in a problem posed by Nachbin.
Quasi-Normable Preduals of Spaces of Holomorphic Functions
1997
Abstract Let H ( U ) denote the space of all holomorphic functions on an open subset U of a separable Frechet space E . Let τ ω denote the compact-ported topology on H ( U ) introduced by Nachbin. Let G ( U ) denote the predual of H ( U ) constructed by Mazet. In our main result we show that E is quasi-normable if and only if G ( U ) is quasi-normable if and only if ( H ( U ), τ ω ) satisfies the strict Mackey convergence condition.
Existence of Unconditional Bases in Spaces of Polynomials and Holomorphic Functions
2002
Our main result shows that every Montel Kothe echelon or coechelon space E of order 1 < p ≤ ∞ is nuclear if and only if for every (some) m ≥ 2 the space ((mE), τ0) of m-homegeneus polynomials on E endowed with the compact-open topology τ0 has an unconditional basis if and only if the space (ℋ(E), τδ) of holomorphic functions on E endowed with the bornological topology τδ associated to τ0 has an unconditional basis (for coechelon spaces τδ equals τ0). The main idea is to extend the concept of the Gordon-Lewis property from Banach to Frechet and (DF) spaces. In this way we obtain techniques which are used to characterize the existence of unconditional basis in spaces of m-th (symmetric) tenso…
Cluster values of holomorphic functions of bounded type
2015
We study the cluster value theorem for Hb(X), the Fréchet algebra of holomorphic functions bounded on bounded sets of X. We also describe the (size of) fibers of the spectrum of Hb(X). Our results are rather complete whenever X has an unconditional shrinking basis and for X = ℓ1. As a byproduct, we obtain results on the spectrum of the algebra of all uniformly continuous holomorphic functions on the ball of ℓ1. Fil: Aron, Richard Martin. Kent State University; Estados Unidos Fil: Carando, Daniel Germán. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentina Fil: Lassalle, S…
Isometries of weighted spaces of holomorphic functions on unbounded domains
2009
We study isometries between weighted spaces of holomorphic functions on unbounded domains in ℂn. We show that weighted spaces of holomorphic functions on unbounded domains may exhibit behaviour different from that observed on bounded domains. We calculate the isometries for specific weights on the complex plane and the right half-plane.
Weyl type theorems for bounded linear operators on Banach spaces
2011
In 1909 H. Weyl [59] studied the spectra of all compact linear perturbations of a self-adjoint operator defined on a Hilbert space and found that their intersection consisted precisely of those points of the spectrum where are not isolated eigenvalues of nite multiplicity. Later, the property established by Weyl for self-adjoint operators has been observed for several other classes of operators, for instance hyponormal operators on Hilbert spaces, Toeplitz operators,convolution operators on group algebras, and many other classes of operators ned on Banach spaces . In the literature, a bounded linear operator defined on a Banach space which satisfies this property is said to satisfy Weyl's t…