Faber-hypercyclic operators

Badea, Cătălin; Grivaux, Sophie

doi:10.1007/s11856-008-1003-4

Cited by 5 publications

(4 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…provided that E is convex and contains W (A). Bounding F n (A) for a suitable E ⊂ C is also of interest for various other tasks, for instance for spectral inclusions [1], Faber hypercyclicity [3], or the approximate computation of matrix functions [6]. In view of (5), we would like E containing σ(A) to be well separated from 0 and to be as small as possible, and thus also allow for non-convex sets.…”

Section: Introduction and Statement Of The Main Resultsmentioning

confidence: 99%

Faber polynomials of matrices for non-convex sets

Beckermann,

Crouzeix

2013

Preprint

View full text Add to dashboard Cite

It has been recently shown that ||Fn(A)|| ≤ 2, where A is a linear continuous operator acting in a Hilbert space, and Fn is the Faber polynomial of degree n corresponding to some convex compact E ⊂ C containing the numerical range of A. Such an inequality is useful in numerical linear algebra, it allows for instance to derive error bounds for Krylov subspace methods.In the present paper we extend this result to not necessary convex sets E.

show abstract

Section: Introduction and Statement Of The Main Resultsmentioning

confidence: 99%

Faber polynomials of matrices for non-convex sets

Beckermann,

Crouzeix

2013

Preprint

View full text Add to dashboard Cite

show abstract

“…Note that in the above theorem, if p = 1, then it will be a Godefroy-Shapiro criterion for mixing operators [1,Theorem 1.3].…”

Section: Definition 4 Let T ∈ B(x)mentioning

confidence: 99%

$k$-bitransitive and compound operators on Banach spaces

Bamerni

Kılıçman

2016

Carpathian Math. Publ.

View full text Add to dashboard Cite

In this this paper, we introduce new classes of operators in complex Banach spaces, which we call k-bitransitive operators and compound operators to study the direct sum of diskcyclic operators. We create a set of sufficient conditions for an operator to be k-bitransitive or compound. We give a relation between topologically mixing operators and compound operators. Also, we extend the Godefroy-Shapiro Criterion for topologically mixing operators to compound operators.

show abstract

“…Faber polynomials appear as a natural generalization of the Taylor polynomials of the disk and play an important role in the approximation theory of functions of one complex variable (see [26]). It appears that in many situations, the operators F n (T ) have the same kind of relationship with the domain Ω or its boundary ∂Ω that the powers T n have with the unit disk D or its boundary T. See [3] for an example of this. Here is the definition of Faber-bounded and partially Faber-bounded operators, which play the role with respect to Ω of power-bounded and partially power-bounded operators.…”

Section: Faber-bounded Operators and ω-Jamison Sequencesmentioning

confidence: 99%

Size of the peripheral point spectrum under power or resolvent growth conditions

Badea¹,

Grivaux²

2007

Journal of Functional Analysis

Self Cite

View full text Add to dashboard Cite

We characterize Jamison sequences, that is sequences (n k ) of positive integers with the following property: every bounded linear operator T acting on a separable Banach space with sup k T n k < +∞ has a countable set of peripheral eigenvalues. We also discuss partially power-bounded operators acting on Banach or Hilbert spaces having peripheral point spectra with large Hausdorff dimension. For a Lavrentiev domain Ω in the complex plane, we show the uniform minimality of some families of eigenvectors associated with peripheral eigenvalues of operators satisfying the Kreiss resolvent condition with respect to Ω. We introduce and study the notion of Ω-Jamison sequence, which is defined by replacing the partial power-boundedness condition sup k T n k < +∞ by sup k F Ω n k (T ) < +∞, where F Ω n is the nth Faber polynomial of Ω. A characterization of Ω-Jamison sequences is obtained for domains with sufficiently smooth boundary.

show abstract

Faber-hypercyclic operators

Cited by 5 publications

References 20 publications

Faber polynomials of matrices for non-convex sets

Faber polynomials of matrices for non-convex sets

$k$-bitransitive and compound operators on Banach spaces

Size of the peripheral point spectrum under power or resolvent growth conditions

Contact Info

Product

Resources

About