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Insomecase, likeinthel p spacesandtheschattenclassess p, we obtain optimal lower bounds, while for other spaces we only give some estimates of the optimal lower bounds. Turett proved a sort of reverse inequality: For more details on the Aron-Berner extension, as well as extensions of polynomials in general, we refer the reader to the survey by I.

We also study desigualdzdes problem on different spaces: The authors found the exact value of c r d and proved that its order is d.

S X We start by showing that g is continuous. El factor problem consiste en buscar cotas inferiores para la norma del producto de polinomios de grados previamente fijados.

## Rodríguez, Jorge Tomás

In particular, this result implies the result of Arias-de-Reyna about the polarization constants mentioned above.

S l d C Now we are ready to prove our main result of this section. So, an alternative procedure is the following: Now we are ready to state our method to obtain lower estimates of c x. X R be a polynomial of degree k. We also obtain some less restrictive conditions for some particular Banach spaces, like the L p spaces or Schatten classes S p. 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.

Let us sketch some of the ideas behind this method. But the restriction of AB T to the diagonal does not depend on the order of the composition.

This result holds for real Hilbert spaces and n 5 see [PR], Theorembut it is not known if it is true for every natural number n. Definition Given k N, a mapping P: In this chapter we also study the factor problem on ultraproducts of Banach spaces.

Unfortunately, this stronger result is not necessarily valid if we choose other sets of unit functionals. To add the widget to Blogger, click here and follow the easy directions provided by Blogger.

These constants have been studied by several authors. Desiguwldades focus mainly on the so called factor problem and plank problem. Remez type inequalities In this section, we introduce Remez type inequalities for polynomials.

### Desigualdades y ecuaciones polinomiales – Factile Jeopardy Classroom Review Game

The factor problem is the problem of finding lower desigyaldades for the norm of the product of polynomials of some prescribed degrees. Facultad de Ciencias Exactas y Naturales. Make your selections below, then copy and paste the code below into your HTML source. Polarization constants of l d p k spaces In this section we apply the method developed in the previous section, stated in Theorem.

In the particular case when X is a Hilbert space, due to the symmetry of the sphere, we may even expect that they are uniformly distributed across the sphere. We devote the first section to develop a method to estimate the polarization constant of a finite dimensional space. With the same argument we may assume that there is x 0 S X such polinomialez x n x polinommiales.

### Jorge Tomás Rodríguez – Google Scholar Citations

We will treat separately the lower and the upper bound. These type of inequalities have been widely studied by several authors in a variety of contexts. Next lemma is a particular case of Lemma. To embed a widget in your blog’s sidebar, install the Wolfram Alpha Widget Sidebar Pluginand copy and paste the Widget ID below into the “id” field:.

Daniel Carando Lugar de trabajo: Luis Federico Leloir, disponible en digital. It is important to remark that this terminology it is not standard an in some works the polarization constant stands for a different constant, see for example [Di] and [LR]. K We need the following auxiliary lemma due to A.

Although these problems are related, they are of an independent interest and will be treated accordingly. Similarly, we can define z: Ball in [Ba1], where he proved slightly more than the following: In the proof of Proposition Enable Javascript to interact with content and submit forms on Wolfram Alpha websites.