Linear Subspaces in Zeros of Polynomials on Banach Spaces

BANACH SPACES OF POLYNOMIALS AS “LARGE” SUBSPACES OF l∞-SPACES

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.

On quasi-complemented subspaces of banach spaces.

Strongly Proximinal Subspaces in Banach Spaces

We give descriptions of SSDand QP -points in C(K)-spaces and use this to characterize strongly proximinal subspaces of finite codimension in L1(μ). We provide some natural class of examples of strongly proximinal subspaces which are not necessarily finite codimensional. We also study transitivity of strong proximinal subspaces of finite codimension.

0 Orlicz - Pettis Polynomials on Banach Spaces

We introduce the class of Orlicz-Pettis polynomials between Banach spaces, defined by their action on weakly unconditionally Cauchy series. We give a number of equivalent definitions, examples and counterexamples which highlight the differences between these polynomials and the corresponding linear operators.

Polynomials on Banach Spaces with Unconditional Bases

We study the classes of homogeneous polynomials on a Banach space with unconditional Schauder basis that have unconditionally convergent monomial expansions relative to this basis. We extend some results of Matos, and we show that the homogeneous polynomials with unconditionally convergent expansions coincide with the polynomials that are regular with respect to the Banach lattices structure of...