Interest in Sobolev type equations has recently increased signi cantly, moreover, there arose a necessity for their consideration in quasi-Banach spaces. The need is dictated not so much by the desire to ll up the theory but by the aspiration to comprehend nonclassical models of mathematical physics in quasi-Banach spaces. Notice that the Sobolev type equations are called evolutionary if soluti...

In this note we study Banach spaces of traces of real polynomials on R to compact subsets equipped with supremum norms from the point of view of Geometric Functional Analysis.

Let X represent either a space C[−1,1] or L α,β(w), 1 ≤ p < ∞, of functions on [−1,1]. It is well known that X are Banach spaces under the sup and the p-norms, respectively. We prove that there exist the best possible normalized Banach subspaces Xα,β of X such that the system of Jacobi polynomials is densely spread on these, or, in other words, each f ∈ Xα,β can be represented by a linear combi...

The Bishop-Phelps theorem [1] states that for any Banach space X, the set of norm attaining linear bounded functionals is dense in X ′, the dual space of X. Since then, the study of norm attaining functions has attracted the attention of many authors. Lindenstrauss showed in [2] that there is no Bishop-Phelps theorem for linear bounded operators. Nevertheless, he proved that the set of bounded ...

In this paper we study some properties related to the biduals of certain Banach spaces whose elements are multilinear functionals, or polynomials, defined in Banach spaces. In particular, we obtain a simple description of the n-fold Schwartz -product. We give examples of Banach spaces that are not quasi-reflexive and so, for each positive integer n, P(nX)∗∗ identifies with P(nX∗∗) in a way clea...