Orbits of linear operators and Banach space geometry

• Autorzy: Jean-Matthieu Augé
• Języki publikacji: EN

Abstrakty

EN

Let T be a bounded linear operator on a (real or complex) Banach space X. If (aₙ) is a sequence of non-negative numbers tending to 0, then the set of x ∈ X such that ||Tⁿx|| ≥ aₙ||Tⁿ|| for infinitely many n's has a complement which is both σ-porous and Haar-null. We also compute (for some classical Banach space) optimal exponents q > 0 such that for every non-nilpotent operator T, there exists x ∈ X such that $(||Tⁿx||/||Tⁿ||) ∉ ℓ^{q}(ℕ )$, using techniques which involve the modulus of asymptotic uniform smoothness of X.

Kategorie tematyczne

• 47A05: General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
• 47A16: Cyclic vectors, hypercyclic and chaotic operators
• 28A05: Classes of sets (Borel fields, σ -rings, etc.), measurable sets, Suslin sets, analytic sets

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2012
• Tom: 212
• Numer: 1
• Strony: 21-39

Daty

wydano

2012

Twórcy

autor

Jean-Matthieu Augé

• Université Bordeaux 1, 351, Cours de la Libération, F-33405 Talence Cedex, France

Identyfikatory

DOI

10.4064/sm212-1-2