Unconditional Convergence of Random Series and the Geometry of Banach Spaces

2000 ◽  
Vol 7 (1) ◽  
pp. 85-96 ◽  
Author(s):  
V. Kvaratskhelia
Keyword(s):  
Banach Spaces ◽  
Unconditional Convergence ◽  
Random Series

Abstract The a.s. unconditionally convergent random series are investigated. The connection of the a.s. unconditionally convergence with the geometry of spaces is established.

Complex convexity and the geometry of Banach spaces

1986 ◽  
Vol 99 (3) ◽  
pp. 495-506 ◽  
Author(s):  
S. J. Dilworth
Keyword(s):  
Banach Spaces ◽  
Present Article ◽  
Uniform Convexity ◽  
Unconditional Convergence

The notion of PL-convexity was introduced in [4]. In the present article several results are proved which related PL-convexity to various aspects of the geometry of Banach spaces. The first section introduces the moduli of comples convexity and makes a comparison with the more familiar modulus of uniform convexity. It is shown that unconditional convergence of implies convergence of . In the next section the moduli and are shown to be related. The method of proof gives rise to a theorem about strict c-convexity of Lp(X) and a result on the representability in Lp(X).

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