Volume 11, Number 1, April 2010, pp. 13-33
Mikio Kato, Kichi-Suke Saito and Takayuki Tamura
Key words:
Absolute norm, convex function, direct sum of Banach spaces, uniformly non-ℓn1 space, uniformly non-square space
Mathematices Subject Classification: 46B20, 46B99

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	Abstract:
	We shall characterize the uniform non-ℓn1-ness of the ψ-direct sum X ⊕ψ Y of Banach spaces X and Y, where ψ is a convex function on the unit interval satisfying certain conditions. A previous result for the uniform non-squareness will be obtained as a corollary. As extreme cases we shall treat the ℓ1-sum and the ℓ∞-sum of finitely many Banach spaces.

Uniform non-ℓn1-ness of ψ-direct sums of Banach spaces

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