An isomorphic characterization of the Schmidt class
We present an extension of the classical isomorphic classification of the Banach spaces C([0,α]) of all real continuous functions defined on the nondenumerable intervals of ordinals [0,α]. As an application, we establish the isomorphic classification of the Banach spaces of all real continuous functions defined on the compact spaces , the topological product of the Cantor cubes with smaller than the first sequential cardinal, and intervals of ordinal numbers [0,α]. Consequently, it is relatively...
We prove that there exist constants C>0 and 0 < λ < 1 so that for all convex bodies K in 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 satisfying . 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.
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...
Estimates of the generalized Stokes resolvent system, i.e. with prescribed divergence, in an infinite cylinder Ω = Σ × ℝ with , a bounded domain of class , are obtained in the space , 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.
For 1 ≤ q < ∞, let 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 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 >...
We construct an example as announced in the title. We also indicate all right, left and two-sided ideals in this example.
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 -space for some 1 ≤ p < ∞.
We find an optimal Sobolev-type space on all of whose functions admit a trace on subspaces of of given dimension. A corresponding trace embedding theorem with sharp range is established.
Let E be a Banach space with a separable dual. Zippin’s theorem asserts that E embeds in a Banach space 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 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 and can be controlled by the Szlenk index of E, where the Szlenk index...
Let f be a function in the Douglas algebra A and let I be a finitely generated ideal in A. We give an estimate for the distance from f to I that allows us to generalize a result obtained by Bourgain for to arbitrary Douglas algebras.