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Random walks on free products

M. Gabriella Kuhn (1991)

Annales de l'institut Fourier

Let G = * j = 1 q + 1 G n j + 1 be the product of q + 1 finite groups each having order n j + 1 and let μ be the probability measure which takes the value p j / n j on each element of G n j + 1 ∖ { e } . In this paper we shall describe the point spectrum of μ in C reg * ( G ) and the corresponding eigenspaces. In particular we shall see that the point spectrum occurs only for suitable choices of the numbers n j . We also compute the continuous spectrum of μ in C reg * ( G ) in several cases. A family of irreducible representations of G , parametrized on the continuous spectrum of μ ,...

Rank α operators on the space C(T,X)

Dumitru Popa (2002)

Colloquium Mathematicae

For 0 ≤ α < 1, an operator U ∈ L(X,Y) is called a rank α operator if x ₙ → τ α x implies Uxₙ → Ux in norm. We give some results on rank α operators, including an interpolation result and a characterization of rank α operators U: C(T,X) → Y in terms of their representing measures.

Retractions onto the Space of Continuous Divergence-free Vector Fields

Philippe Bouafia (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

We prove that there does not exist a uniformly continuous retraction from the space of continuous vector fields onto the subspace of vector fields whose divergence vanishes in the distributional sense. We then generalise this result using the concept of m -charges, introduced by De Pauw, Moonens, and Pfeffer: on any subset X ⊆ ℝ n satisfying a mild geometric condition, there is no uniformly continuous representation operator for m -charges in X .

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