All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 66 Next

Displaying 1301 – 1320 of 13204

Showing per page

An isomorphic Dvoretzky's theorem for convex bodies

Y. Gordon, O. Guédon, M. Meyer (1998)

Studia Mathematica

We prove that there exist constants C>0 and 0 < λ < 1 so that for all convex bodies K in ℝ n with non-empty interior and all integers k so that 1 ≤ k ≤ λn/ln(n+1), there exists a k-dimensional affine subspace Y of ℝ n satisfying d ( Y ∩ K , B 2 k ) ≤ C ( 1 + √ ( k / l n ( n / ( k l n ( n + 1 ) ) ) ) . This formulation of Dvoretzky’s theorem for large dimensional sections is a generalization with a new proof of the result due to Milman and Schechtman for centrally symmetric convex bodies. A sharper estimate holds for the n-dimensional simplex.

An iterative algorithm by viscosity approximation method for mixed equilibrium problems, variational inclusion and fixed point of an infinite family of pseudo-contractive mappings

Phayap Katchang, Poom Kumam (2011)

Banach Center Publications

The purpose of this paper is to investigate the problem of finding a common element of the set of solutions for mixed equilibrium problems, the set of solutions of the variational inclusion problems for inverse strongly monotone mappings and the set of common fixed points for an infinite family of strictly pseudo-contractive mappings in the setting of Hilbert spaces. We prove the strong convergence theorem by using the viscosity approximation method for finding the common element of the above four...

An L q ( L ² ) -theory of the generalized Stokes resolvent system in infinite cylinders

Reinhard Farwig, Myong-Hwan Ri (2007)

Studia Mathematica

Estimates of the generalized Stokes resolvent system, i.e. with prescribed divergence, in an infinite cylinder Ω = Σ × ℝ with Σ ⊂ ℝ n - 1 , a bounded domain of class C 1 , 1 , are obtained in the space L q ( ℝ ; L ² ( Σ ) ) , q ∈ (1,∞). As a preparation, spectral decompositions of vector-valued homogeneous Sobolev spaces are studied. The main theorem is proved using the techniques of Schauder decompositions, operator-valued multiplier functions and R-boundedness of operator families.

An M q ( ) -functional calculus for power-bounded operators on certain UMD spaces

Earl Berkson, T. A. Gillespie (2005)

Studia Mathematica

For 1 ≤ q < ∞, let q ( ) denote the Banach algebra consisting of the bounded complex-valued functions on the unit circle having uniformly bounded q-variation on the dyadic arcs. We describe a broad class ℐ of UMD spaces such that whenever X ∈ ℐ, the sequence space ℓ²(ℤ,X) admits the classes q ( ) as Fourier multipliers, for an appropriate range of values of q > 1 (the range of q depending on X). This multiplier result expands the vector-valued Marcinkiewicz Multiplier Theorem in the direction q >...

An operator characterization of L p -spaces in a class of Orlicz spaces

Maciej Burnecki (2008)

Banach Center Publications

We consider an embedding of the group of invertible transformations of [0,1] into the algebra of bounded linear operators on an Orlicz space. We show that if this embedding preserves the group action then the Orlicz space is an L p -space for some 1 ≤ p < ∞.

An optimal endpoint trace embedding

Andrea Cianchi, Luboš Pick (2010)

Annales de l’institut Fourier

We find an optimal Sobolev-type space on ℝ n all of whose functions admit a trace on subspaces of ℝ n of given dimension. A corresponding trace embedding theorem with sharp range is established.

An ordinal version of some applications of the classical interpolation theorem

Benoît Bossard (1997)

Fundamenta Mathematicae

Let E be a Banach space with a separable dual. Zippin’s theorem asserts that E embeds in a Banach space E 1 with a shrinking basis, and W. J. Davis, T. Figiel, W. B. Johnson and A. Pełczyński have shown that E is a quotient of a Banach space E 2 with a shrinking basis. These two results use the interpolation theorem established by W. J. Davis, T. Figiel, W. B. Johnson and A. Pełczyński. Here, we prove that the Szlenk indices of E 1 and E 2 can be controlled by the Szlenk index of E, where the Szlenk index...

Currently displaying 1301 – 1320 of 13204