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Une nouvelle classe d'espaces de Banach vérifiant le théorème de Grothendieck

Gilles Pisier (1978)

Annales de l'institut Fourier

Soit W un espace ℒ 1 et soit R un sous-espace réflexif de dimension infinie de W . Nous montrons que le quotient W / R vérifie le théorème de Grothendieck, c’est-à-dire que tout opérateur de W / R dans un espace de Hilbert est 1-sommant; par ailleurs, W / R n’est pas un espace ℒ 1 . Cela permet de répondre négativement à une question de Lindenstrauss-Pełczyński ainsi qu’à une question similaire de Grothendieck.

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].

Uniform bounds for the bilinear Hilbert transforms (II).

Xiaochun Li (2006)

Revista Matemática Iberoamericana

We continue the investigation initiated in [Grafakos, L. and Li, X.: Uniform bounds for the bilinear Hilbert transforms (I). Ann. of Math. (2)159 (2004), 889-933] of uniform Lp bounds for the family of bilinear Hilbert transformsHα,β(f,g)(x) = p.v. ∫R f(x - αt) g (x - βt) dt/t.

Uniformly bounded composition operators in the banach space of bounded (p, k)-variation in the sense of Riesz-Popoviciu

Francy Armao, Dorota Głazowska, Sergio Rivas, Jessica Rojas (2013)

Open Mathematics

We prove that if the composition operator F generated by a function f: [a, b] × ℝ → ℝ maps the space of bounded (p, k)-variation in the sense of Riesz-Popoviciu, p ≥ 1, k an integer, denoted by RV(p,k)[a, b], into itself and is uniformly bounded then RV(p,k)[a, b] satisfies the Matkowski condition.

Uniformly convergent adaptive methods for a class of parametric operator equations∗

Claude Jeffrey Gittelson (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

We derive and analyze adaptive solvers for boundary value problems in which the differential operator depends affinely on a sequence of parameters. These methods converge uniformly in the parameters and provide an upper bound for the maximal error. Numerical computations indicate that they are more efficient than similar methods that control the error in a mean square sense.

Uniformly convergent adaptive methods for a class of parametric operator equations∗

Claude Jeffrey Gittelson (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

We derive and analyze adaptive solvers for boundary value problems in which the differential operator depends affinely on a sequence of parameters. These methods converge uniformly in the parameters and provide an upper bound for the maximal error. Numerical computations indicate that they are more efficient than similar methods that control the error in a mean square sense.

Uniformly ergodic A-contractions on Hilbert spaces

Laurian Suciu (2009)

Studia Mathematica

We study the concept of uniform (quasi-) A-ergodicity for A-contractions on a Hilbert space, where A is a positive operator. More precisely, we investigate the role of closedness of certain ranges in the uniformly ergodic behavior of A-contractions. We use some known results of M. Lin, M. Mbekhta and J. Zemánek, and S. Grabiner and J. Zemánek, concerning the uniform convergence of the Cesàro means of an operator, to obtain similar versions for A-contractions. Thus, we continue the study of A-ergodic...

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