Operators on spaces of analytic functions

K. Seddighi

Displaying similar documents to “Operators on spaces of analytic functions”

A note on spaces of type $H^{\infty} + C$

David Stegenga (1975)

Annales de l'institut Fourier

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We show that a theorem of Rudin, concerning the sum of closed subspaces in a Banach space, has a converse. By means of an example we show that the result is in the nature of best possible.

On the analyticity of generalized eigenfunctions (case of real variables)

Eberhard Gerlach (1968)

Annales de l'institut Fourier

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On démontre que, dans les espaces fonctionnels propres de Hilbert (avec un noyau reproduisant), formés de fonctions analytiques de $n$ variables dans un domaine $G$ , pour tout opérateur auto-adjoint, les fonctions propres généralisées sont des fonctions réelles-analytiques dans $G$ .

On the multiplication operators on spaces of analytic functions

B. Yousefi, S. Foroutan (2005)

Studia Mathematica

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We consider Hilbert spaces of analytic functions on a plane domain Ω and multiplication operators on such spaces induced by functions from $H^{\infty} (Ω)$ . Recently, K. Zhu has given conditions under which the adjoints of multiplication operators on Hilbert spaces of analytic functions belong to the Cowen-Douglas classes. In this paper, we provide some sufficient conditions which give the converse of the main result obtained by K. Zhu. We also characterize the commutant of certain multiplication operators. ...

Intertwining Multiplication Operators on Function Spaces

Bahman Yousefi, Leila Bagheri (2006)

Bulletin of the Polish Academy of Sciences. Mathematics

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Suppose that X is a Banach space of analytic functions on a plane domain Ω. We characterize the operators T that intertwine with the multiplication operators acting on X.

A perturbation of Lomonosov's theorem

Peter Rosenthal (1982)

Banach Center Publications

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Invariant subspaces on multiply connected domains.

Ali Abkar, Hakan Hedenmalm (1998)

Publicacions Matemàtiques

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The lattice of invariant subspaces of several Banach spaces of analytic functions on the unit disk, for example the Bergman spaces and the Dirichlet spaces, have been studied recently. A natural question is to what extent these investigations carry over to analogously defined spaces on an annulus. We consider this question in the context of general Banach spaces of analytic functions on finitely connected domains Ω. The main result reads as follows: Assume that B is a Banach space of...

Bounded point evaluations for multicyclic operators

M. EL Guendafi, M. Mbekhta, E. H. Zerouali (2005)

Banach Center Publications

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Let T be a multicyclic operator defined on some Banach space. Bounded point evaluations and analytic bounded point evaluations for T are defined to generalize the cyclic case. We extend some known results on cyclic operators to the more general setting of multicyclic operators on Banach spaces. In particular we show that if T satisfies Bishop’s property (β), then $ℬ_{a} = ℬ ∖ σ_{a p} (T)$ . We introduce the concept of analytic structures and we link it to different spectral quantities. We apply this concept...

Analytic and $C^{k}$ approximations of norms in separable Banach spaces

Robert Deville, Vladimir Fonf, Petr Hájek (1996)

Studia Mathematica

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On operators T such that f(T) is hypercyclic.

Teresa Bermúdez, Vivien G. Miller (2000)

Extracta Mathematicae

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Co-analytic, right-invertible operators are supercyclic

Sameer Chavan (2010)

Colloquium Mathematicae

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Let denote a complex, infinite-dimensional, separable Hilbert space, and for any such Hilbert space , let () denote the algebra of bounded linear operators on . We show that for any co-analytic, right-invertible T in (), αT is hypercyclic for every complex α with $| α | > β^{- 1}$ , where $β \equiv i n f_{| | x | | = 1} | | T * x | | > 0$ . In particular, every co-analytic, right-invertible T in () is supercyclic.

A notion of analytic generator for groups of unbounded operators

José E. Galé (2005)

Banach Center Publications

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We introduce a notion of analytic generator for groups of unbounded operators, on Banach modules, arising from Esterle’s quasimultiplier theory. Characterizations of analytic generators are given in terms of the existence of certain functional calculi. This extends recent results about C₀ groups of bounded operators. The theory is applicable to sectorial operators, representations of $H^{\infty}$ , and integrated groups.

Linearity in non-linear problems.

Richard Aron, Domingo García, Manuel Maestre (2001)

RACSAM

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Estudiamos algunas situaciones donde encontramos un problema que, a primera vista, parece no tener solución. Pero, de hecho, existe un subespacio vectorial grande de soluciones del mismo.

Compact endomorphisms of $H^{\infty} (D)$

Joel Feinstein, Herbert Kamowitz (1999)

Studia Mathematica

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Compact composition operators on $H^{\infty} (G)$ , where G is a region in the complex plane, and the spectra of these operators were described by D. Swanton ( Compact composition operators on B(D), Proc. Amer. Math. Soc. 56 (1976), 152-156). In this short note we characterize all compact endomorphisms, not necessarily those induced by composition operators, on $H^{\infty} (D)$ , where D is the unit disc, and determine their spectra.

The structure of Lindenstrauss-Pełczyński spaces

Jesús M. F. Castillo, Yolanda Moreno, Jesús Suárez (2009)

Studia Mathematica

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Lindenstrauss-Pełczyński (for short ℒ) spaces were introduced by these authors [Studia Math. 174 (2006)] as those Banach spaces X such that every operator from a subspace of c₀ into X can be extended to the whole c₀. Here we obtain the following structure theorem: a separable Banach space X is an ℒ-space if and only if every subspace of c₀ is placed in X in a unique position, up to automorphisms of X. This, in combination with a result of Kalton [New York J. Math. 13 (2007)], provides...