On multicyclic operators

Herrero, Domingo A.

doi:10.1007/bf01682740

Cited by 45 publications

(21 citation statements)

References 17 publications

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“…Similarly, if S is a semi-Fredholm operator such that σ(5) = σ(R) and ind S = h E Z', then S 7* R, whence we conclude that ρf_ F is discontinuous at R for all possible sets Σ. D According to [7] (Theorem 4 and its proof), given A in £(%), a point λ Gσ^) Π 3σ(,4),ε>0and/? ε β(ϋC), ||A|| < 1, there exists Λ(λ, ε, R) unitarily equivalent to…”

Section: Theorem 1 (I) σ 0 Is Continuous At a Et(%) If And Only If σ(mentioning

confidence: 75%

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Continuity of spectral functions and the lakes of Wada

Herrero¹

1984

Pacific J. Math.

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Section: Theorem 1 (I) σ 0 Is Continuous At a Et(%) If And Only If σ(mentioning

confidence: 75%

“…It was observed in [3] that both, σ and o w , are continuous on a dense subset and discontinuous on a dense subset (this last result depending on the proof of Theorem 4 in [7]). …”

Section: Theorem 1 (I) σ 0 Is Continuous At a Et(%) If And Only If σ(mentioning

confidence: 93%

Continuity of spectral functions and the lakes of Wada

Herrero¹

1984

Pacific J. Math.

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“…Proof. Since T is m-multicyclic, nullity(T * ) = m ( [14]). Moreover, by Corollary 3.4, one has H = {null(T * − µI) : µ ∈ D r } for all r > 0.…”

Section: Preliminaries In This Paper We Discuss the Following Fundamentioning

confidence: 99%

On operators close to isometries

Chavan

2008

Studia Math.

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Abstract. We introduce and discuss a class of operators, to be referred to as operators close to isometries. The Bergman-type operators, 2-hyperexpansions, expansive pisometries, and certain alternating hyperexpansions are main examples of such operators. We establish a few decomposition theorems for operators close to isometries. Applications are given to the theory of p-isometries and of hyperexpansive operators. Preliminaries. In this paper, we discuss the following fundamental problems from single-variable operator theory. If S in B(H) is a completely non-unitary left-invertible operator, under what conditions does• S * admit a complete set of eigenvectors?• S possess the wandering subspace property?• S admit a complete set of almost eigenvectors?Recall that an operator S in B(H) admits a complete set of eigenvectors if H = {f ∈ H : (S − µI)f = 0 for some µ ∈ C} and that S possesses the wandering subspace property ifA left-invertible operator S in B(H) admits a complete set of almost eigenvectors ifOne of the main results of this paper asserts that if a completely nonunitary S in B(H) is close to isometry, then S * admits a complete set of eigenvectors. Moreover, under some additional hypotheses, such an S possesses the wandering subspace property as well as a complete set of almost 2000 Mathematics Subject Classification: Primary 47A16, 47B20.

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“…Therefore Proposition 3.1 shows that the spectral multiplicity of T F does not exceed N. On the other hand, the spectral multiplicity of an arbitrary operator T is greater than or equal to max dim Ker(T *&*) (see [9]). K This is not a best-possible result that guarantees that the commutant of a Toeplitz operator is abelian.…”

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confidence: 93%

Dual Piecewise Analytic Bundle Shift Models of Linear Operators

Yakubovich

1996

Journal of Functional Analysis

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Let T be a Banach space operator with empty point spectrum, whose essential spectrum lies on a finite system of (possibly intersecting) curves. Under certain conditions on T, dual analytic representations of T as a kind of bundle shift and of T* as an``adjoint bundle shift'' are constructed. A specialization of this scheme is given, which allows one to obtain in some cases concrete similarity models of T and T* in certain analogues of Smirnov E 2 -spaces. The latter construction is applied to Toeplitz operators with smooth symbols.1996 Academic Press, Inc. IntroductionAlthough the spectral nature of many types of nonnormal operators such as contractions, dissipative operators, and the like is now well understood, still very little is known about operators with their essential spectra``in the general position.'' The aim of this paper is to present a way to construct a kind of diagonalization similarity model for a special class of operators whose essential spectra are rather thin.Let T be a (bounded) linear operator on a reflexive Banach space X. It will be assumed that T behaves like the shift operator, that is, that the eigenvalues of T * fill in some connected components of the complement of the essential spectrum _ ess (T ), whereas the point spectrum of T is empty. The main steps of the construction of dual similarity models for T and T * are as follows.Fix an auxiliary operator J: X* Ä R acting into a finite-dimensional space R. (Let us agree that the adjoint B* to a Banach or linear topological space B is the space of linear continuous article no. 0032

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On multicyclic operators

Cited by 45 publications

References 17 publications

Continuity of spectral functions and the lakes of Wada

Continuity of spectral functions and the lakes of Wada

On operators close to isometries

Dual Piecewise Analytic Bundle Shift Models of Linear Operators

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