For any , we construct a concrete 1-parameter family of non-orbit equivalent actions of the free group . These actions arise as diagonal products between a generalized Bernoulli action and the action , where is seen as a subgroup of .
Let A be a unital Banach function algebra with character space . For , let and be the ideals of functions vanishing at x and in a neighbourhood of x, respectively. It is shown that the hull of is connected, and that if x does not belong to the Shilov boundary of A then the set has an infinite connected subset. Various related results are given.
An ideal in a commutative topological algebra with separately continuous multiplication is non-removable if and only if it consists locally of joint topological divisors of zero. Also, any family of non-removable ideals can be removed simultanously.
The aim of this paper, is to introduce the convex structure (specially, Takahashi convex structure) on modular spaces. Moreover, we are interested in proving some common fixed point theorems for non-self mappings in modular space.
It is shown that if (S,∑,m) is an atomless finite measure space and X is a Banach space without the Radon-Nikodym property, then the quotient space cabv(∑,m;X)/L¹(m;X) is nonseparable.
We show that an infinite-dimensional complete linear space X has: ∙ a dense hereditarily Baire Hamel basis if |X| ≤ ⁺; ∙ a dense non-meager Hamel basis if for some cardinal κ.
We introduce and investigate a class of non-separable tree-like Banach spaces. As a consequence, we prove that we cannot achieve a satisfactory extension of Rosenthal's ℓ₁-theorem to spaces of the type ℓ₁(κ) for κ an uncountable cardinal.
We show that in for p ≠ 2 the constants of equivalence between finite initial segments of the Walsh and trigonometric systems have power type growth. We also show that the Riemann ideal norms connected with those systems have power type growth.
The main purpose of the present paper is to extend the theory of non-smooth atomic decompositions to anisotropic function spaces of Besov and Triebel-Lizorkin type. Moreover, the detailed analysis of the anisotropic homogeneity property is carried out. We also present some results on pointwise multipliers in special anisotropic function spaces.
We prove that for a real analytic generic submanifold of whose Levi-form has constant rank, the tangential -system is non-solvable in degrees equal to the numbers of positive and negative Levi-eigenvalues. This was already proved in [1] in case the Levi-form is non-degenerate (with non-necessarily real analytic). We refer to our forthcoming paper [7] for more extensive proofs.