Displaying similar documents to “Compact endomorphisms of H ( D )

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 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 ( 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. ...

-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 -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.

Spectra of weighted composition operators on algebras of analytic functions on Banach spaces

Cheng Yuan, Ze-Hua Zhou (2011)

Czechoslovak Mathematical Journal

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Let E be a complex Banach space, with the unit ball B E . We study the spectrum of a bounded weighted composition operator u C ϕ on H ( B E ) determined by an analytic symbol ϕ with a fixed point in B E such that ϕ ( B E ) is a relatively compact subset of E , where u is an analytic function on B E .

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 a = σ a p ( T ) . We introduce the concept of analytic structures and we link it to different spectral quantities. We apply this concept...

On the norm-closure of the class of hypercyclic operators

Christoph Schmoeger (1997)

Annales Polonici Mathematici

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Let T be a bounded linear operator acting on a complex, separable, infinite-dimensional Hilbert space and let f: D → ℂ be an analytic function defined on an open set D ⊆ ℂ which contains the spectrum of T. If T is the limit of hypercyclic operators and if f is nonconstant on every connected component of D, then f(T) is the limit of hypercyclic operators if and only if f ( σ W ( T ) ) z : | z | = 1 is connected, where σ W ( T ) denotes the Weyl spectrum of T.

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...

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 B ( X ) satisfying the relation σ T 1 ( x ) = σ T 2 ( x ) for any vector x X , where σ T ( x ) denotes the local spectrum of T B ( X ) at the point x 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 0 as n . Without these conditions, we describe the operators with the same local spectra only in some particular cases.

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 , and integrated groups.

A new characterization of Anderson’s inequality in C 1 -classes

S. Mecheri (2007)

Czechoslovak Mathematical Journal

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Let be a separable infinite dimensional complex Hilbert space, and let ( ) denote the algebra of all bounded linear operators on into itself. Let A = ( A 1 , A 2 , , A n ) , B = ( B 1 , B 2 , , B n ) be n -tuples of operators in ( ) ; we define the elementary operators Δ A , B ( ) ( ) by Δ A , B ( X ) = i = 1 n A i X B i - X . In this paper, we characterize the class of pairs of operators A , B ( ) satisfying Putnam-Fuglede’s property, i.e, the class of pairs of operators A , B ( ) such that i = 1 n B i T A i = T implies i = 1 n A i * T B i * = T for all T 𝒞 1 ( ) (trace class operators). The main result is the equivalence between this property and the...

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 , | | · | | X ) and ( Y , | | · | | 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 f ) | | Y 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.

Composition operators: N α to the Bloch space to Q β

Jie Xiao (2000)

Studia Mathematica

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Let N α ,B and Qβ be the weighted Nevanlinna space, the Bloch space and the Q space, respectively. Note that B and Q β are Möbius invariant, but N α is not. We characterize, in function-theoretic terms, when the composition operator C ϕ f = f ϕ induced by an analytic self-map ϕ of the unit disk defines an operator C ϕ : N α B , B Q β , N α Q β which is bounded resp. compact.

Lie algebras generated by Jordan operators

Peng Cao, Shanli Sun (2008)

Studia Mathematica

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It is proved that if J i is a Jordan operator on a Hilbert space with the Jordan decomposition J i = N i + Q i , where N i is normal and Q i is compact and quasinilpotent, i = 1,2, and the Lie algebra generated by J₁,J₂ is an Engel Lie algebra, then the Banach algebra generated by J₁,J₂ is an Engel algebra. Some results for normal operators and Jordan operators on Banach spaces are given.

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 C t - 1 , t > 0, for a continuous time semigroup ( e t A ) t 0 , a bounded operator T is called analytic if the discrete time semigroup ( T n ) n satisfies ( T - I ) T n 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 ϱ ( T ) 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 C ( ω + n - 1 ) e ω n , n ∈ ℕ. As an application...

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 × l 4 / 3 l such that none of the associated linear operators...

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 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.