Author Keywords: Bounded in probability; convergence in probability; cotype; uniform tightness condition 相似文献
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1.
Jeff D. Farmer 《Israel Journal of Mathematics》1994,87(1-3):257-273
We ask when the space ofN-homogeneous analytic polynomials on a Banach space is reflexive. This turns out to be related to whether polynomials are
weakly sequentially continuous, and to the geometry of spreading models. For example, if these spaces are reflexive for allN, no quotient of the dual space may have a spreading model with an upperq-estimate, and every bounded holomorphic function on the unit ball has a Taylor series made up of weakly sequentially continuous
polynomials (we assume the approximation property). Alencar, Aron and Dineen [AAD] gave the first example of some properties
of a polynomially reflexive space (usingT*, the original Tsirelson space); we show that these properties and others are shared by all polynomially reflexive spaces.
This paper forms a portion of the Ph. D. dissertation of the author, under the supervision of W. B. Johnson. 相似文献
2.
M. Zippin 《Israel Journal of Mathematics》1968,6(1):74-79
LetX be a Banach space with a basis. It is proved that if (a) all bases ofX are shrinking, or (b) all bases ofX are boundedly complete, thenX is reflexive.
Research supported by Grant AF EOAR 66-18.
This is part of the author’s Ph.D. thesis prepared at The Hebrew University of Jerusalem, under the supervision of Professor
A. Dvoretzky and Professor J. Lindenstrauss. The author wishes to thank Professor Lindenstrauss for his valuable remarks. 相似文献
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Daniel C. Kemp 《Mathematische Annalen》1975,218(3):211-217
5.
B. Satco 《Journal of Mathematical Analysis and Applications》2007,332(2):1460-1467
In the present paper we focus on a generalization of the notion of integral convexity. This concept, introduced in [J.Y. Wang, Y.M. Ma, The integral convexity of sets and functionals in Banach spaces, J. Math. Anal. Appl. 295 (2004) 211-224] by replacing, in the definition of classical notion of convexity, the sum by the integral, has interesting applications in optimal control problems. By using, instead of Bochner integral, a more general vector integral, that of Pettis, we obtain some results on integral-extreme points of subsets of a Banach space stronger than those given in [J.Y. Wang, Y.M. Ma, The integral convexity of sets and functionals in Banach spaces, J. Math. Anal. Appl. 295 (2004) 211-224]. Finally, a natural example coming from measure theory is included, in order to reflect the relationships between different kinds of integral convexity. 相似文献
6.
Two simple concepts are presented for constructing necessary and sufficient compactness criteria in Banach spaces. The concepts are applied to the spaces lip(T), C(T), and Lp(µ), where T is a compact metric space. 相似文献
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László Lempert 《Periodica Mathematica Hungarica》2008,56(2):241-245
Given a complex Banach space X and a holomorphic function f on its unit ball B, we discuss the problem whether f can be approximated, uniformly on smaller balls, by functions g holomorphic on all of X.
Research partially supported by NSF grant DMS0700281. 相似文献
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Jon K. Cole 《Journal of Optimization Theory and Applications》1972,9(3):214-215
The existence of a strongly measurable function taking its values in a variable subset of a separable and reflexive Banach space was shown in Ref. 1. Here, we show the collection of all such functions to be weakly compact in itself. 相似文献
12.
J.L. Ansorena 《Quaestiones Mathematicae》2018,41(5):615-628
We revisit the concept of a subsymmetric norm and construct a subsymmetric renorming of a Banach space with a subsymmetric basis. As a by-product of our work we introduce the concept of a lower symmetric basis and investigate its connection with subsymmetric bases and subsymmetric renormings. 相似文献
13.
By a ball-covering B of a Banach space X, we mean that B is a collection of open (or closed) balls off the origin whose union contains the unit sphere SX of X; and X is said to have the ball-covering property (BCP) provided it admits a ball-covering by countably many balls. In this note we give a natural example showing that the ball-covering property of a Banach space is not inherited by its subspaces; and we present a sharp quantitative version of the recent Fonf and Zanco renorming result saying that if the dual X∗ of X is w∗ separable, then for every ε>0 there exist a (1+ε)-equivalent norm on X, and an R>0 such that in this new norm SX admits a ball-covering by countably many balls of radius R. Namely, we show that R=R(ε) can be taken arbitrarily close to (1+ε)/ε, and that for X=?1[0,1] the corresponding R cannot be equal to 1/ε. This gives the sharp order of magnitude for R(ε) as ε→0. 相似文献
14.
Marcus Waurick 《PAMM》2014,14(1):987-988
In this short note we discuss the causality of linear closable operators in reflexive Banach spaces. We show that in general causality is not preserved under closure procedures. We shall give an alternative definition of causality for closable operators by means of a certain continuity poperty that carries over to the closure. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
15.
In this paper, we give conditions under which the powers of the multiplication operator \(M_{z}\) are reflexive on a Banach space of functions analytic on a plane domain. 相似文献
16.
For every open subset G of
and for every continuous, strictly positive weight v on G, the Banach space
of all the holomorphic functions f on
G such that
vanishes at infinity on G, endowed with the natural weighted
sup-norm, is isomorphic to a closed subspace of the Banach
space c0; hence it is reflexive if and only if it is finite
dimensional.Received: 30 September 2002 相似文献
17.
We shall give a necessary and sufficient condition for uniformly integrable martingales to converge in the norm topology in a Banach function space. This yields a new characterization of the probabilisticA p -condition introduced by Izumisawa and Kazamaki [4]. 相似文献
18.
We prove that weakly Lindelöf determined Banach spaces are characterized by the existence of a “full” projectional generator. Some other results pertaining to this class of Banach spaces are given. 相似文献
19.
Isabel Marrero 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(18):6890-6894
In this short note we prove that a Banach space X is reflexive if, and only if, the Eisenfeld–Lakshmikantham measure of nonconvexity in X satisfies the Cantor property. Using this characterization, some results in best approximation and fixed point theory for reflexive Banach spaces are generalized by removing convexity requirements. 相似文献
20.
Xiang Chen Wang 《Statistics & probability letters》1990,10(5):391-396
Let B be a separable Banach space. The following is one of the results proved in this paper. The Banach space B is of cotype p if and only if
1. dn, n 1, has no subsequence converging in probability, and
2. ∑n 1|an|p < ∞ whenever ∑n 1andn converges almost surely are equivalent for every sequence dn, n 1, of symmetric independent random elements taking values in B.