A note on the inverse function theorem of Nash and Moser.
Duality of a large family of analytic function spaces.
Weakly compact composition operators on analytic vector-valued function spaces.
A Characterization of Schwartz Spaces.
Schwartz spaces and compact holomorphic mappings.
Homomorphisms on C...(E) and C...-bounding Sets.
Applications of Ultraproducts to Infinite Dimensional Holomorphy.
Sets of interpolation and sampling for weighted Banach spaces of holomorphic functions
We give an elementary approach which allows us to evaluate Seip's conditions characterizing interpolating and sampling sequences in weighted Bergman spaces of infinite order for a wide class of weights depending on the distance to the boundary of the domain. Our results also give some information on cases not covered by Seip's theory. Moreover, we obtain new criteria for weights to be essential.
Algebras of real analytic functions: Homomorphisms and bounding sets
This article deals with bounding sets in real Banach spaces E with respect to the functions in A(E), the algebra of real analytic functions on E, as well as to various subalgebras of A(E). These bounding sets are shown to be relatively weakly compact and the question whether they are always relatively compact in the norm topology is reduced to the study of the action on the set of unit vectors in of the corresponding functions in . These results are achieved by studying the homomorphisms on the...
Compact homomorphisms between algebras of analytic functions
We prove that every weakly compact multiplicative linear continuous map from into is compact. We also give an example which shows that this is not generally true for uniform algebras. Finally, we characterize the spectra of compact composition operators acting on the uniform algebra , where is the open unit ball of an infinite-dimensional Banach space E.
Spectral properties of weighted composition operators on the Bloch and Dirichlet spaces
The spectra of invertible weighted composition operators on the Bloch and Dirichlet spaces are studied. In the Bloch case we obtain a complete description of the spectrum when φ is a parabolic or elliptic automorphism of the unit disc. In the case of a hyperbolic automorphism φ, exact expressions for the spectral radii of invertible weighted composition operators acting on the Bloch and Dirichlet spaces are derived.
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