Vector-valued walsh-paley martingales and geometry of banach spaces
نویسندگان
چکیده
منابع مشابه
Vector–valued Walsh–Paley martingales and geometry of Banach spaces
Abstract The concept of Rademacher type p (1 ≤ p ≤ 2) plays an important role in the local theory of Banach spaces. In [3] Mascioni considers a weakening of this concept and shows that for a Banach space X weak Rademacher type p implies Rademacher type r for all r < p. As with Rademacher type p and weak Rademacher type p, we introduce the concept of Haar type p and weak Haar type p by replacing...
متن کاملLower estimates of random unconditional constants of Walsh-Paley martingales with values in Banach spaces
for all n = 1, 2, ... and all martingales {Mk}0 ⊂ L X p with values in X . It turns out that this definition is equivalent to the modified one if we replace ”for all 1 < p < ∞” by ”for some 1 < p < ∞”, and ”for all martingales” by ”for all Walsh-Paley-martingales” (see [3] for a survey). Motivated by these definitions we investigate Banach spaces X by means of the sequences {RUMDn(X)}n=1 wherea...
متن کاملCompactness in Vector-valued Banach Function Spaces
We give a new proof of a recent characterization by Diaz and Mayoral of compactness in the Lebesgue-Bochner spaces L X , where X is a Banach space and 1 ≤ p < ∞, and extend the result to vector-valued Banach function spaces EX , where E is a Banach function space with order continuous norm. Let X be a Banach space. The problem of describing the compact sets in the Lebesgue-Bochner spaces LpX , ...
متن کاملOperator Valued Series and Vector Valued Multiplier Spaces
Let $X,Y$ be normed spaces with $L(X,Y)$ the space of continuous linear operators from $X$ into $Y$. If ${T_{j}}$ is a sequence in $L(X,Y)$, the (bounded) multiplier space for the series $sum T_{j}$ is defined to be [ M^{infty}(sum T_{j})={{x_{j}}in l^{infty}(X):sum_{j=1}^{infty}% T_{j}x_{j}text{ }converges} ] and the summing operator $S:M^{infty}(sum T_{j})rightarrow Y$ associat...
متن کاملMean Convergence of Vector–valued Walsh Series
Given any Banach space X, let L X 2 denote the Banach space of all measurable functions f : [0, 1] → X for which f 2 := 1 0 f (t) 2 dt
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: Israel Journal of Mathematics
سال: 1997
ISSN: 0021-2172,1565-8511
DOI: 10.1007/bf02774024