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Displaying 121 – 134 of 134

On the spectrum of the operator which is a composition of integration and substitution

Ignat Domanov (2008)

Studia Mathematica

Let ϕ: [0,1] → [0,1] be a nondecreasing continuous function such that ϕ(x) > x for all x ∈ (0,1). Let the operator $V_{ϕ} : f (x) \mapsto \int_{0}^{ϕ (x)} f (t) d t$ be defined on L₂[0,1]. We prove that $V_{ϕ}$ has a finite number of nonzero eigenvalues if and only if ϕ(0) > 0 and ϕ(1-ε) = 1 for some 0 < ε < 1. Also, we show that the spectral trace of the operator $V_{ϕ}$ always equals 1.

On the spectrum of $ψ$ -contracting operators.

Al-Nayef, Anwar A. (2001)

Journal of Applied Mathematics and Stochastic Analysis

On the Spherical Spectrum.

Jose I. Nieto (1980)

Manuscripta mathematica

On the topological boundary of the one-sided spectrum

Vladimír Müller (1999)

Czechoslovak Mathematical Journal

It is well-known that the topological boundary of the spectrum of an operator is contained in the approximate point spectrum. We show that the one-sided version of this result is not true. This gives also a negative answer to a problem of Schmoeger.

On the weak decomposition property $(δ_{w})$

El Hassan Zerouali, Hassane Zguitti (2005)

Studia Mathematica

We study a new class of bounded linear operators which strictly contains the class of bounded linear operators with the decomposition property (δ) or the weak spectral decomposition property (weak-SDP). We treat general local spectral properties for operators in this class and compare them with the case of operators with (δ).

On totally $*$ -paranormal operators

Eungil Ko, Hae-Won Nam, Young Oh Yang (2006)

Czechoslovak Mathematical Journal

In this paper we study some properties of a totally $*$ -paranormal operator (defined below) on Hilbert space. In particular, we characterize a totally $*$ -paranormal operator. Also we show that Weyl’s theorem and the spectral mapping theorem hold for totally $*$ -paranormal operators through the local spectral theory. Finally, we show that every totally $*$ -paranormal operator satisfies an analogue of the single valued extension property for $W^{2} (D, H)$ and some of totally $*$ -paranormal operators have scalar extensions....

Opening gaps in the spectrum of strictly ergodic Schrödinger operators

Artur Avila, Jairo Bochi, David Damanik (2012)

Journal of the European Mathematical Society

We consider Schrödinger operators with dynamically defined potentials arising from continuous sampling along orbits of strictly ergodic transformations. The Gap Labeling Theorem states that the possible gaps in the spectrum can be canonically labelled by an at most countable set defined purely in terms of the dynamics. Which labels actually appear depends on the choice of the sampling function; the missing labels are said to correspond to collapsed gaps. Here we show that for any collapsed gap,...

Opérateur de Schrödinger pour un champ magnétique constant sur l'espace euclidien à deux dimensions

Yves Colin de Verdière (1983/1984)

Séminaire de théorie spectrale et géométrie

Opérateurs de Riesz dont le coeur analytique est fermé

Widad Bouamama (2004)

Studia Mathematica

Dans ce travail nous donnons plusieurs caractérisations, en termes spectraux, d'opérateurs de Riesz dont le coeur analytique est fermé. Notamment, nous montrons que pour un opérateur de Riesz T, le coeur analytique est fermé si et seulement si sa dimension est finie si et seulement si zéro est isolé dans le spectre de T si et seulement si T = Q + F avec QF = FQ = 0, F de rang fini et Q quasinilpotent. Ce dernier résultat montre qu'un opérateur de Riesz dont le coeur analytique est fermé admet la...

Operatori di Riesz generalizzati su spazi di Banach

P. Aiena, U. Oliveri (1979)

Rendiconti del Seminario Matematico della Università di Padova

Operators on a Hilbert space similar to a part of the backward shift of multiplicity one

Yoichi Uetake (2001)

Studia Mathematica

Let A: X → X be a bounded operator on a separable complex Hilbert space X with an inner product $⟨ \cdot, \cdot ⟩_{X}$ . For b, c ∈ X, a weak resolvent of A is the complex function of the form $⟨ {(I - z A)}^{- 1} b, c ⟩_{X}$ . We will discuss an equivalent condition, in terms of weak resolvents, for A to be similar to a restriction of the backward shift of multiplicity 1.

Operators with an ergodic power

Teresa Bermúdez, Manuel González, Mostafa Mbekhta (2000)

Studia Mathematica

We prove that if some power of an operator is ergodic, then the operator itself is ergodic. The converse is not true.

Operator-Valued Ultradistributions in the Spectral Theory.

Ioana Cioranescu (1976)

Mathematische Annalen

Original title unknown

Issledovanija po prikladnoj matematike

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