A notion of analytic generator for groups of unbounded operators

José E.  Galé

Displaying similar documents to “A notion of analytic generator for groups of unbounded operators”

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.

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. ...

$^{\infty}$ -vectors and boundedness

Jan Stochel, F. H. Szafraniec (1997)

Annales Polonici Mathematici

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The following two questions as well as their relationship are studied: (i) Is a closed linear operator in a Banach space bounded if its $^{\infty}$ -vectors coincide with analytic (or semianalytic) ones? (ii) When are the domains of two successive powers of the operator in question equal? The affirmative answer to the first question is established in case of paranormal operators. All these investigations are illustrated in the context of weighted shifts.

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.

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...

Besov spaces and 2-summing operators

M. A. Fugarolas (2004)

Colloquium Mathematicae

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Let Π₂ be the operator ideal of all absolutely 2-summing operators and let $I_{m}$ be the identity map of the m-dimensional linear space. We first establish upper estimates for some mixing norms of $I_{m}$ . Employing these estimates, we study the embedding operators between Besov function spaces as mixing operators. The result obtained is applied to give sufficient conditions under which certain kinds of integral operators, acting on a Besov function space, belong to Π₂; in this context, we also...

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.

Absolutely continuous linear operators on Köthe-Bochner spaces

(2011)

Banach Center Publications

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Let E be a Banach function space over a finite and atomless measure space (Ω,Σ,μ) and let $(X, | | \cdot | |_{X})$ and $(Y, | | \cdot | |_{Y})$ be real Banach spaces. A linear operator T acting from the Köthe-Bochner space E(X) to Y is said to be absolutely continuous if $| | T (1_{A ₙ} f) {| |}_{Y} \to 0$ whenever μ(Aₙ) → 0, (Aₙ) ⊂ Σ. In this paper we examine absolutely continuous operators from E(X) to Y. Moreover, we establish relationships between different classes of linear operators from E(X) to Y.

Modulation space estimates for multilinear pseudodifferential operators

Árpád Bényi, Kasso A. Okoudjou (2006)

Studia Mathematica

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We prove that for symbols in the modulation spaces $ℳ^{p, q}$ , p ≥ q, the associated multilinear pseudodifferential operators are bounded on products of appropriate modulation spaces. In particular, the symbols we study here are defined without any reference to smoothness, but rather in terms of their time-frequency behavior.

Multiple summing operators on $l_{p}$ spaces

Dumitru Popa (2014)

Studia Mathematica

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We use the Maurey-Rosenthal factorization theorem to obtain a new characterization of multiple 2-summing operators on a product of $l_{p}$ spaces. This characterization is used to show that multiple s-summing operators on a product of $l_{p}$ spaces with values in a Hilbert space are characterized by the boundedness of a natural multilinear functional (1 ≤ s ≤ 2). We use these results to show that there exist many natural multiple s-summing operators $T : l_{4 / 3} \times l_{4 / 3} \to l ₂$ such that none of the associated linear operators...

Perturbation of analytic operators and temporal regularity of discrete heat kernels

Sönke Blunck (2000)

Colloquium Mathematicae

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In analogy to the analyticity condition $∥ A e^{t A} ∥ \leq C t^{- 1}$ , t > 0, for a continuous time semigroup ${(e^{t A})}_{t \geq 0}$ , a bounded operator T is called analytic if the discrete time semigroup ${(T^{n})}_{n \in ℕ}$ satisfies $∥ (T - I) T^{n} ∥ \leq C n^{- 1}$ , n ∈ ℕ. We generalize O. Nevanlinna’s characterization of powerbounded and analytic operators T to the following perturbation result: if S is a perturbation of T such that $∥ R (λ_{0}, T) - R (λ_{0}, S) ∥$ is small enough for some $λ_{0} \in ϱ (T) \cap ϱ (S)$ , then the type $ω$ of the semigroup $(e^{t (S - I)})$ also controls the analyticity of S in the sense that $∥ (S - I) S^{n} ∥ \leq C (ω + n^{- 1}) e^{ω n}$ , n ∈ ℕ. As an application...

On operators with the same local spectra

Aleksandar Torgašev (1998)

Czechoslovak Mathematical Journal

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Let $B (X)$ be the algebra of all bounded linear operators in a complex Banach space $X$ . We consider operators $T_{1}, T_{2} \in B (X)$ satisfying the relation $σ_{T_{1}} (x) = σ_{T_{2}} (x)$ for any vector $x \in X$ , where $σ_{T} (x)$ denotes the local spectrum of $T \in B (X)$ at the point $x \in X$ . We say then that $T_{1}$ and $T_{2}$ have the same local spectra. We prove that then, under some conditions, $T_{1} - T_{2}$ is a quasinilpotent operator, that is $∥ {(T_{1} - T_{2})}^{n} ∥^{1 / n} \to 0$ as $n \to \infty$ . Without these conditions, we describe the operators with the same local spectra only in some particular cases.

Subharmonic functions in sub-Riemannian settings

Andrea Bonfiglioli, Ermanno Lanconelli (2013)

Journal of the European Mathematical Society

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In this paper we furnish mean value characterizations for subharmonic functions related to linear second order partial differential operators with nonnegative characteristic form, possessing a well-behaved fundamental solution $Γ$ . These characterizations are based on suitable average operators on the level sets of $Γ$ . Asymptotic characterizations are also considered, extending classical results of Blaschke, Privaloff, Radó, Beckenbach, Reade and Saks. We analyze as well the notion of subharmonic...

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

Robert Deville, Vladimir Fonf, Petr Hájek (1996)

Studia Mathematica

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Degenerate evolution problems and Beta-type operators

Antonio Attalienti, Michele Campiti (2000)

Studia Mathematica

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The present paper is concerned with the study of the differential operator Au(x):=α(x)u”(x)+β(x)u’(x) in the space C([0,1)] and of its adjoint Bv(x):=((αv)’(x)-β(x)v(x))’ in the space $L^{1} (0, 1)$ , where α(x):=x(1-x)/2 (0≤x≤1). A careful analysis of their main properties is carried out in view of some generation results available in [6, 12, 20] and [25]. In addition, we introduce and study two different kinds of Beta-type operators as a generalization of similar operators defined in [18]. Among...

Regularity of sets with constant intrinsic normal in a class of Carnot groups

Marco Marchi (2014)

Annales de l’institut Fourier

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In this Note, we define a class of stratified Lie groups of arbitrary step (that are called “groups of type $☆$ ” throughout the paper), and we prove that, in these groups, sets with constant intrinsic normal are vertical halfspaces. As a consequence, the reduced boundary of a set of finite intrinsic perimeter in a group of type $☆$ is rectifiable in the intrinsic sense (De Giorgi’s rectifiability theorem). This result extends the previous one proved by Franchi, Serapioni & Serra Cassano...

Operators on spaces of analytic functions

K. Seddighi (1994)

Studia Mathematica

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Let $M_{z}$ be the operator of multiplication by z on a Banach space of functions analytic on a plane domain G. We say that $M_{z}$ is polynomially bounded if $∥ M_{p} ∥ \leq C ∥ p ∥_{G}$ for every polynomial p. We give necessary and sufficient conditions for $M_{z}$ to be polynomially bounded. We also characterize the finite-codimensional invariant subspaces and derive some spectral properties of the multiplication operator in case the underlying space is Hilbert.

Divergence of general operators on sets of measure zero

G. A. Karagulyan (2010)

Colloquium Mathematicae

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We consider sequences of linear operators Uₙ with a localization property. It is proved that for any set E of measure zero there exists a set G for which $U ₙ_{G} (x)$ diverges at each point x ∈ E. This result is a generalization of analogous theorems known for the Fourier sum operators with respect to different orthogonal systems.

On a proof of the boundedness and nuclearity of pseudodifferential operators in $R^{n}$

Jan A. Rempała (1990)

Annales Polonici Mathematici

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Regularity of domains of parameterized families of closed linear operators

Teresa Winiarska, Tadeusz Winiarski (2003)

Annales Polonici Mathematici

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The purpose of this paper is to provide a method of reduction of some problems concerning families $A_{t} = {(A (t))}_{t \in}$ of linear operators with domains ${(_{t})}_{t \in}$ to a problem in which all the operators have the same domain . To do it we propose to construct a family ${(Ψ_{t})}_{t \in}$ of automorphisms of a given Banach space X having two properties: (i) the mapping $t \mapsto Ψ_{t}$ is sufficiently regular and (ii) $Ψ_{t} () =_{t}$ for t ∈ . Three effective constructions are presented: for elliptic operators of second order with the Robin boundary condition...

On ergodicity for operators with bounded resolvent in Banach spaces

Kirsti Mattila (2011)

Studia Mathematica

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We prove results on ergodicity, i.e. on the property that the space is a direct sum of the kernel of an operator and the closure of its range, for closed linear operators A such that ${| | α (α - A)}^{- 1} | |$ is uniformly bounded for all α > 0. We consider operators on Banach spaces which have the property that the space is complemented in its second dual space by a projection P. Results on ergodicity are obtained under a norm condition ||I - 2P|| ||I - Q|| < 2 where Q is a projection depending on the...