scholarly journals Uniform convexity of ψ-direct sums of Banach spaces

2003 ◽  
Vol 277 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Kichi-Suke Saito ◽  
Mikio Kato
Keyword(s):  
Banach Spaces ◽  
Uniform Convexity ◽  
Direct Sums

On Ψ direct sums of Banach spaces and convexity

2003 ◽  
Vol 75 (3) ◽  
pp. 413-422 ◽  
Author(s):  
Mikio Kato ◽  
Kichi-Suke Saito ◽  
Takayuki Tamura
Keyword(s):  
Convex Function ◽  
Banach Spaces ◽  
Convex Set ◽  
Uniform Convexity ◽  
Direct Sums ◽  
Direct Sum ◽  
Continuous Convex Function

AbstractLet X1, X2, …, XN be Banach spaces and ψ a continuous convex function with some appropriate conditions on a certain convex set in RN−1. Let (X1⊕X2⊕…⊕XN)Ψ be the direct sum of X1, X2, …, XN equipped with the norm associated with Ψ. We characterize the strict, uniform, and locally uniform convexity of (X1 ⊕ X2 ⊕ … ⊕ XN)Ψ; by means of the convex function Ψ. As an application these convexities are characterized for the ℓp, q-sum (X1 ⊕ X2 ⊕ … ⊕ XN)p, q (1 < q ≤ p ≤ ∈, q < ∞), which includes the well-known facts for the ℓp-sum (X1 ⊕ X2 ⊕ … ⊕ XN)p in the case p = q.

Countable Direct Sums of Banach Spaces

1989 ◽  
Vol 141 (1) ◽  
pp. 73-79
Author(s):  
M. Valdivia
Keyword(s):  
Banach Spaces ◽  
Direct Sums

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).

scholarly journals Deviation from weak Banach–Saks property for countable direct sums

2014 ◽  
Vol 68 (2) ◽  
Author(s):  
Andrzej Kryczka
Keyword(s):  
Banach Spaces ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Direct Sums ◽  
Bounded Linear

AbstractWe introduce a seminorm for bounded linear operators between Banach spaces that shows the deviation from the weak Banach-Saks property. We prove that if (X

Strict convexity of absolute norms on and direct sums of banach spaces

2002 ◽  
Vol 2002 (2) ◽  
pp. 209507 ◽  
Author(s):  
Yasuji Takahashi ◽  
Mikio Kato ◽  
Kichi-Suke Saito
Keyword(s):  
Banach Spaces ◽  
Strict Convexity ◽  
Direct Sums

Multiplicity of direct sums of operators on Banach spaces

2009 ◽  
Vol 41 (6) ◽  
pp. 1041-1052
Author(s):  
Sophie Grivaux ◽  
Maria Roginskaya
Keyword(s):  
Banach Spaces ◽  
Direct Sums
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