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Later, as a corollary of Theorem 3 from [BST], it was obtained that the optimal Desigualaddes n with such property, for complex Banach spaces, is n n. Recall that, as pointed out in Remark 1. All the Banach spaces considered will be either over the complex field C or the real field R, we write K when we mean either.

To add the widget to Blogger, click here and follow the easy directions provided by Blogger. The author also presented a similar question to Tarski s Plank Problem. Ball in [Ba1], where he proved slightly more than the following: A Banach space X is finite Make your selections below, then copy and paste the code below into your HTML source. This document is part of the doctoral theses collection of the Central Library Dr.


Unfortunately, this stronger result is not necessarily valid if we choose other sets of unit functionals. We also give some estimates on the norm of the product of linear functions on l d Cthus obtaining bounds for the nth polarization constant c n l d C.

Jorge Tomás Rodríguez – Google Scholar Citations

The following is the main result of this section and gives the asymptotic behaviour of the polarization constants c l d p k as d goes to infinity. We devote Chapter to analyze these constants. For the upper bound, using Jensen s inequality and equality 0.

This problem has been studied in several spaces, considering a wide variety of norms. We call such measures admissible.

Ganzburg studied Remez type inequalities for polynomials on several variables in [BG]. In the particular case when X is a real Hilbert space of dimension d we write B d and S d 1 instead. In order to prove Theorem. To add the widget to iGoogle, click here. For every natural number m define g m: In order to do this we will polinomialds with measures satisfying a not too restrictive property.

Desigualdaes follows, by a complexification argument, that for a real Hilbert space the nth polarization constant is at most n n see [RS]. In particular, in Functional Analysis, the study of multilinear forms and polynomials has been growing in the last decades.

These sets of linear functions may not be the ones that give equality in. The Mahler measure of a polynomial Desigualcades We consider the product of linear functions i.


In order to introduce the notion of polynomials on Banach spaces we start by 7.

Jorge Tomás Rodríguez – Google 학술검색 서지정보

Por su interminable paciencia y estar siempre desigualdaded para aconsejarme y asistirme. We are interested in inequalities similar to desigualaddes.

Other quantities related to polynomials can be compared with the Mahler measure, such as the norm of a polynomial and its length defined below. The authors found the exact value of c r d and proved that its order is d. Save to My Widgets.

In Chapter 4 we exploit the inequalities presented in [BST, P], as well as the results regarding the factor problem obtained in Chapter 3, to address these kind of polynomial plank problems.

For details on this classical result, as well as a deeper introduction polinomiiales polynomials on Banach spaces, we refer the reader to the survey by Richard Aron [Arn] on this topic. Here, the word plank stands for a set contained between two parallel hyperplanes.