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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 function in Beurling-Orlicz and central Morrey-Orlicz spaces

Lech Maligranda, Katsuo Matsuoka (2015)

Colloquium Mathematicae

We define Beurling-Orlicz spaces, weak Beurling-Orlicz spaces, Herz-Orlicz spaces, weak Herz-Orlicz spaces, central Morrey-Orlicz spaces and weak central Morrey-Orlicz spaces. Moreover, the strong-type and weak-type estimates of the Hardy-Littlewood maximal function on these spaces are investigated.

Maximal regularity for a class of integro-differential equations with infinite delay in Banach spaces

Valentin Keyantuo, Carlos Lizama (2005)

Studia Mathematica

We use Fourier multiplier theorems to establish maximal regularity results for a class of integro-differential equations with infinite delay in Banach spaces. Concrete equations of this type arise in viscoelasticity theory. Results are obtained for periodic solutions in the vector-valued Lebesgue and Besov spaces. An application to semilinear equations is considered.

Maximal regularity, the local inverse function theorem, and local well-posedness for the curve shortening flow

Sahbi Boussandel, Ralph Chill, Eva Fašangová (2012)

Czechoslovak Mathematical Journal

Local well-posedness of the curve shortening flow, that is, local existence, uniqueness and smooth dependence of solutions on initial data, is proved by applying the Local Inverse Function Theorem and L 2 -maximal regularity results for linear parabolic equations. The application of the Local Inverse Function Theorem leads to a particularly short proof which gives in addition the space-time regularity of the solutions. The method may be applied to general nonlinear evolution equations, but is presented...

Maximality of dual coactions on sectional C*-algebras of Fell bundles and applications

Alcides Buss, Siegfried Echterhoff (2015)

Studia Mathematica

We give a simple proof of the maximality of dual coactions on full cross-sectional C*-algebras of Fell bundles over locally compact groups. This result was only known for discrete groups or for saturated (separable) Fell bundles over locally compact groups. Our proof, which is derived as an application of the theory of universal generalised fixed-point algebras for weakly proper actions, is different from these previously known cases and works for general Fell bundles over locally compact groups....

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