Search results for "Holomorph"
showing 10 items of 111 documents
HOLOMORPHIC SUPERPOSITION OPERATORS BETWEEN BANACH FUNCTION SPACES
2013
AbstractWe prove that for a large class of Banach function spaces continuity and holomorphy of superposition operators are equivalent and that bounded superposition operators are continuous. We also use techniques from infinite dimensional holomorphy to establish the boundedness of certain superposition operators. Finally, we apply our results to the study of superposition operators on weighted spaces of holomorphic functions and the$F(p, \alpha , \beta )$spaces of Zhao. Some independent properties on these spaces are also obtained.
Homomorphisms between Algebras of Holomorphic Functions
2014
For two complex Banach spaces X and Y, in this paper, we study the generalized spectrum M-b(X,Y) of all nonzero algebra homomorphisms from H-b(X), the algebra of all bounded type entire functions on X into H-b(Y). We endow M-b(X,Y) with a structure of Riemann domain over L(X*,Y*) whenever.. is symmetrically regular. The size of the fibers is also studied. Following the philosophy of ( Aron et al., 1991), this is a step to study the set M-b,M-infinity (X,B-Y) of all nonzero algebra homomorphisms from Hb(b) (X) into H-infinity (B-Y) of bounded holomorphic functions on the open unit ball of Y and M-infinity(B-X,B-Y) of all nonzero algebra homomorphisms from H-infinity(B-X) into H infinity (B-Y…
Hilbert-Schmidt Hankel operators on the Segal-Bargmann space
2004
This paper considers Hankel operators on the Segal-Bargmann space of holomorphic functions onCn\mathbb {C}^nthat are square integrable with respect to the Gaussian measure. It is shown that in the case of a bounded symbolg∈L∞(Cn)g \in L^{\infty }(\mathbb {C}^n)the Hankel operatorHgH_gis of the Hilbert-Schmidt class if and only ifHg¯H_{\bar {g}}is Hilbert-Schmidt. In the case where the symbol is square integrable with respect to the Lebesgue measure it is known that the Hilbert-Schmidt norms of the Hankel operatorsHgH_gandHg¯H_{\bar {g}}coincide. But, in general, if we deal with bounded symbols, only the inequality‖Hg‖HS≤2‖Hg¯‖HS\|H_g\|_{HS}\leq 2\|H_{\bar {g}}\|_{HS}can be proved. The resul…
Boundedness of composition operators in holomorphic Hölder type spaces
2021
Mean ergodic composition operators on Banach spaces of holomorphic functions
2016
[EN] Given a symbol cc, i.e., a holomorphic endomorphism of the unit disc, we consider the composition operator C-phi(f) = f circle phi defined on the Banach spaces of holomorphic functions A(D) and H-infinity(D). We obtain different conditions on the symbol phi which characterize when the composition operator is mean ergodic and uniformly mean ergodic in the corresponding spaces. These conditions are related to the asymptotic behavior of the iterates of the symbol. Finally, we deal with some particular case in the setting of weighted Banach spaces of holomorphic functions.
Spaces of holomorphic functions in regular domains
2009
AbstractLet Ω be a regular domain in the complex plane C, Ω≠C. Let Gb(Ω) be the linear space over C of the holomorphic functions f in Ω such that f(n) is bounded in Ω and is continuously extendible to the closure Ω¯ of Ω, n=0,1,2,… . We endow Gb(Ω), in a natural manner, with a structure of Fréchet space and we obtain dense subspaces F of Gb(Ω), with good topological linear properties, also satisfying that each function f of F, distinct from zero, does not extend holomorphically outside Ω.
Holomorphic Maps and Pencils of Circles
2008
(2008). Holomorphic Maps and Pencils of Circles. The American Mathematical Monthly: Vol. 115, No. 8, pp. 690-700.
The Composition Operation on Spaces of Holomorphic Mappings
2020
AbstractWe discuss the continuity of the composition on several spaces of holomorphic mappings on open subsets of a complex Banach space. On the Fréchet space of entire mappings that are bounded on bounded sets, the composition turns out to be even holomorphic. In such a space, we consider linear subspaces closed under left and right composition. We discuss the relationship of such subspaces with ideals of operators and give several examples of them. We also provide natural examples of spaces of holomorphic mappings where the composition is not continuous.