scholarly journals How slowly can a bounded sequence cluster?

2012 ◽  
Vol 46 (2) ◽  
pp. 195-204
Author(s):  
John Bentin
2008 ◽  
Vol 683 (1) ◽  
pp. 33-44 ◽  
Author(s):  
B. C. Hsieh ◽  
H. K. C. Yee ◽  
H. Lin ◽  
M. D. Gladders ◽  
D. G. Gilbank

2015 ◽  
Vol 58 (3) ◽  
pp. 507-518
Author(s):  
Ming-Hsiu Hsu ◽  
Ming-Yi Lee

AbstractIn this paper we define a space VMO𝒫 associated with a family 𝒫 of parabolic sections and show that the dual of VMO𝒫 is the Hardy space . As an application, we prove that almost everywhere convergence of a bounded sequence in implies weak* convergence


1975 ◽  
Vol 27 (2) ◽  
pp. 418-422 ◽  
Author(s):  
C. L. Anderson ◽  
W. H. Hyams ◽  
C. K. McKnight

Suppose x = (x∝) is a net with values in a metric space X having metric ρ. If a point z in X can be found to minimizethen z is called a center point (c.p.) of x. The space X is (netwise) c.p. complete if every bounded net has at least one c.p.; it is sequentially c.p. complete if every bounded sequence has a c.p. Netwise c.p. completeness implies sequential c.p. completeness, and the latter implies completeness since any c.p. of a Cauchy sequence will necessarily be a limit point of that sequence.These notions are related to the set centers of Calder et al. [2].


1974 ◽  
Vol 15 (1) ◽  
pp. 63-65 ◽  
Author(s):  
John Bibby

A bounded monotonic sequence is convergent. This paper shows that a bounded sequence which is g-monotonic (to be defined) also converges. The proof generalises one attributed to Professor R. A. Rankin by Copson [1]. The theorem requires two definitions: the first axiomatises the notion of “average“ and the second generalises the concept of monotonicity.


2002 ◽  
Vol 577 (2) ◽  
pp. 595-603 ◽  
Author(s):  
Henk Hoekstra ◽  
Howard K. C. Yee ◽  
Michael D. Gladders

2005 ◽  
Vol 36 (4) ◽  
pp. 706-709 ◽  
Author(s):  
A.K. Hicks ◽  
E. Ellingson ◽  
M. Bautz ◽  
H.K.C. Yee ◽  
M. Gladders ◽  
...  

2010 ◽  
Vol 411 (1) ◽  
pp. L51-L55 ◽  
Author(s):  
Simon J. Murphy ◽  
Warrick A. Lawson ◽  
Michael S. Bessell ◽  
Daniel D. R. Bayliss

Sign in / Sign up

Export Citation Format

Share Document