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Maximal abelian subalgebras and projections in two Banach algebras associated with a topological dynamical system

Marcel de Jeu, Jun Tomiyama (2012)

Studia Mathematica

If Σ = (X,σ) is a topological dynamical system, where X is a compact Hausdorff space and σ is a homeomorphism of X, then a crossed product Banach *-algebra ℓ¹(Σ) is naturally associated with these data. If X consists of one point, then ℓ¹(Σ) is the group algebra of the integers. The commutant C(X)₁' of C(X) in ℓ¹(Σ) is known to be a maximal abelian subalgebra which has non-zero intersection with each non-zero closed ideal, and the same holds for the commutant C(X)'⁎ of C(X) in C*(Σ), the enveloping...

Maximal inequalities and Riesz transform estimates on L p spaces for Schrödinger operators with nonnegative potentials

Pascal Auscher, Besma Ben Ali (2007)

Annales de l’institut Fourier

We show various L p estimates for Schrödinger operators - Δ + V on n and their square roots. We assume reverse Hölder estimates on the potential, and improve some results of Shen. Our main tools are improved Fefferman-Phong inequalities and reverse Hölder estimates for weak solutions of - Δ + V and their gradients.

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