Related papers: Dominated polynomials on infinite dimensional spac…

The main goal of this note is to establish a connection between the cotype of the Banach space X and the parameters r for which every 2-homogeneous polynomial on X is r-dominated. Let cotX be the infimum of the cotypes assumed by X and…

In this paper we study the maximal subspaces of continuous n-homogeneous polynomials on complex and real non separable Banach spaces. In the real case we will prove that if P is a 2-homogeneous polynomial and if there exist a k-dimensional…

We prove a number of decoupling inequalities for nonhomogeneous random polynomials with coefficients in Banach space. Degrees of homogeneous components enter into comparison as exponents of multipliers of terms of certain Poincar\'e-type…

We study the dynamics induced by homogeneous polynomials on Banach spaces. It is known that no homogeneous polynomial defined on a Banach space can have a dense orbit. We show, a simple and natural example of a homogeneous polynomial with…

We lift upper and lower estimates from linear functionals to $n$-homogeneous polynomials and using this result show that $l_\infty$ is finitely represented in the space of $n$-homogeneous polynomials, $n\ge2$, for any infinite dimensional…

We present an infinite dimensional Banach space in which the set of hyperbolic linear isomorphisms in that space is not dense (in the norm topology) in the set of linear isomorphisms.

In this article, we study the multi-dimensional Bohr radii of holomorphic functions defined on the Banach sequence spaces with values in the Banach spaces. For the case of finite dimensional Banach spaces, we exhibit the exact asymptotic…

We prove that weakly unconditionally Cauchy (w.u.C.) series and unconditionally converging (u.c.) series are preserved under the action of polynomials or holomorphic functions on Banach spaces, with natural restrictions in the latter case.…

We study lower bounds for the norm of the product of polynomials and their applications to the so called \emph{plank problem.} We are particularly interested in polynomials on finite dimensional Banach spaces, in which case our results…

We provide two examples of complex homogeneous quadratic polynomials P on Banach spaces of the form l_1(I). The first polynomial P has both separable and nonseparable maximal zero subspaces. The second polynomial P has the property that…

We study two-dimensional Banach spaces with polynomial numerical indices equal to zero.

Classes of homogeneous polynomials between Banach spaces have been studied in the last three decades from the perspective of the so-called ideal property: if a polynomial P belongs to a class Q, then the composition u o P o v of P with…

This paper is concerned with the study of $M$-structures in spaces of polynomials. More precisely, we discuss for $E$ and $F$ Banach spaces, whether the class of weakly continuous on bounded sets $n$-homogeneous polynomials, $\mathcal…

Let $F$ be an algebraically closed field of characteristic different from $2$. We show that the images of multilinear $*$-polynomials on $UT_2$ are homogeneous vector spaces. An analogous result holds for $UT_3$ endowed with non-trivial…

Ideals of polynomials and multilinear operators between Banach spaces have been exhaustively investigated in the last decades. In this paper, we introduce a unified (and more general) approach and propose some lines of investigation in this…

This work explores the interaction between different norms in infinite-dimensional vector spaces, focusing on their impact on Banach space structures and topological properties. We examine norms induced by bijective linear maps, the…

The main goal of this paper is to characterize arbitrary nonlinear (non-multilinear) mappings $f:X_{1}\times...\times X_{n}\rightarrow Y$ between Banach spaces that satisfy a quite natural Pietsch Domination-type theorem around a given…

Spaces of homogeneous polynomials on a Banach space are frequently equipped with quasinorms instead of norms. In this paper we develop a technique to replace the original quasi-norm by a norm in a dual preserving way, in the sense that the…

The $m$-symmetric Macdonald polynomials form a basis of the space of polynomials that are symmetric in the variables $x_{m+1},x_{m+2},\dots$ (while having no special symmetry in the variables $x_1,\dots,x_m$).We establish in this article…

For $1< p <2$ we obtain sharp inequalities for the supremum of products of homogeneous polynomials on $L_p(\mu)$, whenever the number of factors is no greater than the dimension of these Banach spaces (a condition readily satisfied in the…