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Unicellularity of the multiplication operator on Banach spaces of formal power series

B. Yousefi (2001)

Studia Mathematica

Let β ( n ) n = 0 ∞ be a sequence of positive numbers and 1 ≤ p < ∞. We consider the space ℓ p ( β ) of all power series f ( z ) = ∑ n = 0 ∞ f ̂ ( n ) z ⁿ such that ∑ n = 0 ∞ | f ̂ ( n ) | p | β ( n ) | p < ∞ . We give some sufficient conditions for the multiplication operator, M z , to be unicellular on the Banach space ℓ p ( β ) . This generalizes the main results obtained by Lu Fang [1].

Universal Jamison spaces and Jamison sequences for C₀-semigroups

Vincent Devinck (2013)

Studia Mathematica

An increasing sequence ( n k ) k ≥ 0 of positive integers is said to be a Jamison sequence if for every separable complex Banach space X and every T ∈ ℬ(X) which is partially power-bounded with respect to ( n k ) k ≥ 0 , the set σ p ( T ) ∩ is at most countable. We prove that for every separable infinite-dimensional complex Banach space X which admits an unconditional Schauder decomposition, and for any sequence ( n k ) k ≥ 0 which is not a Jamison sequence, there exists T ∈ ℬ(X) which is partially power-bounded with respect to ( n k ) k ≥ 0 and has the...

Variations on Yano's extrapolation theorem.

David E. Edmunds, Miroslav Krbec (2005)

Revista Matemática Complutense

We give very short and transparent proofs of extrapolation theorems of Yano type in the framework of Lorentz spaces. The decomposition technique developed in Edmunds-Krbec (2000) enables us to obtain known and new results in a unified manner.

Weighted shift operators on lp spaces.

Lucas Jódar (1986)

Stochastica

The analytic-spectral structure of the commutant of a weighted shift operator defined on a lp space (1 ≤ p &lt; ∞) is studied. The cases unilateral, bilateral and quasinilpotent are treated. We apply the results to study certain questions related to unicellularity, strictly cyclicity and the existence of hyperinvariant subspaces.

Weyl product algebras and classical modulation spaces

Anders Holst, Joachim Toft, Patrik Wahlberg (2010)

Banach Center Publications

We discuss continuity properties of the Weyl product when acting on classical modulation spaces. In particular, we prove that M p , q is an algebra under the Weyl product when p ∈ [1,∞] and 1 ≤ q ≤ min(p,p’).

Why the Riesz transforms are averages of the dyadic shifts?

Stefanie Petermichl, Serguei Treil, Alexander L. Volberg (2002)

Publicacions Matemàtiques

The first author showed in [18] that the Hilbert transform lies in the closed convex hull of dyadic singular operators - so called dyadic shifts. We show here that the same is true in any Rn - the Riesz transforms can be obtained as the results of averaging of dyadic shifts. The goal of this paper is almost entirely methodological: we simplify the previous approach, rather than presenting the new one.[Proceedings of the 6th International Conference on Harmonic Analysis and Partial Differential Equations,...

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