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Orbits of linear operators and Banach space geometry

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Augé J.-M.

Studia Mathematica

2012

tom 212

nr 1

21-39

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.

Ograniczanie wyników

1 Studia Mathematica

1 Augé J.-M.

1 2012

Wyniki wyszukiwania

Orbits of linear operators and Banach space geometry