Uniform asymptotic smoothness of norms
نویسندگان
چکیده
منابع مشابه
Smoothness, asymptotic smoothness and the Blum-Hanson property
We isolate various sufficient conditions for a Banach space X to have the so-called Blum-Hanson property. In particular, we show that X has the Blum-Hanson property if either the modulus of asymptotic smoothness of X has an extremal behaviour at infinity, or if X is uniformly Gâteaux smooth and embeds isometrically into a Banach space with a 1-unconditional finite-dimensional decomposition.
متن کاملAsymptotic behavior of mean uniform norms for sequences of Gaussian processes and fields
We consider the mean uniform (mixed) norms for a sequence of Gaussian random functions. For a wide class of Gaussian processes and fields the (2 log n)1/2-asymptotic for mixed norms is found whenever the volume of the index set is of order n and tends to infinity, for example, n-length time interval for random processes. Some numerical examples demonstrate the rate of convergence for the obtain...
متن کاملStrong Martingale Type and Uniform Smoothness
Abstract. We introduce stronger versions of the usual notions of martingale type p ≤ 2 and cotype q ≥ 2 of a Banach space X and show that these concepts are equivalent to uniform p-smoothness and q-convexity, respectively. All these are metric concepts, so they depend on the particular norm in X. These concepts allow us to get some more insight into the fine line between X being isomorphic to a...
متن کاملAbsolutely Representing Systems, Uniform Smoothness and Type
Absolutely representing system (ARS) in a Banach space X is a set D ⊂ X such that every vector x in X admits a representation by an absolutely convergent series x = ∑ i aixi with (ai) ⊂ R and (xi) ⊂ D. We investigate some general properties of ARS. In particular, ARS in uniformly smooth and in B-convex Banach spaces are characterized via ε-nets of the unit balls. Every ARS in a B-convex Banach ...
متن کاملProducts of Polynomials in Uniform Norms
We study inequalities connecting a product of uniform norms of polynomials with the norm of their product. This subject includes the well known Gel’fond-Mahler inequalities for the unit disk and Kneser inequality for the segment [−1, 1]. Using tools of complex analysis and potential theory, we prove a sharp inequality for norms of products of algebraic polynomials over an arbitrary compact set ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1986
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700004032