On Bernstein type rational functions of two variables
We present some results concerning the problem , in , , where , , and is a smooth bounded domain containing the origin. In particular, bifurcation and uniqueness results are discussed.
This survey features some recent developments concerning the bounded approximation property in Banach spaces. As a central theme, we discuss the weak bounded approximation property and the approximation property which is bounded for a Banach operator ideal. We also include an overview around the related long-standing open problem: Is the approximation property of a dual Banach space always metric?
Commuting multi-contractions of class and having a regular isometric dilation are studied. We prove that a polydisc contraction of class is the restriction of a backwards multi-shift to an invariant subspace, extending a particular case of a result by R. E. Curto and F.-H. Vasilescu. A new condition on a commuting multi-operator, which is equivalent to the existence of a regular isometric dilation and improves a recent result of A. Olofsson, is obtained as a consequence.
One of the most important methods used in literature to introduce new properties in a Banach space E, consists in establishing some non trivial relationships between different classes of subsets of E. For instance, E is reflexive, or has finite dimension, if and only if every bounded subset is weakly relatively compact or norm relatively compact, respectively.On the other hand, Banach spaces of the type C(K) and Lp(μ) play a vital role in the general theory of Banach spaces. Their structure is so...