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On complemented copies of c₀(ω₁) in C(Kⁿ) spaces

Leandro Candido, Piotr Koszmider (2016)

Studia Mathematica

Given a compact Hausdorff space K we consider the Banach space of real continuous functions C(Kⁿ) or equivalently the n-fold injective tensor product ̂ ε n C ( K ) or the Banach space of vector valued continuous functions C(K,C(K,C(K...,C(K)...). We address the question of the existence of complemented copies of c₀(ω₁) in ̂ ε n C ( K ) under the hypothesis that C(K) contains such a copy. This is related to the results of E. Saab and P. Saab that X ̂ ε Y contains a complemented copy of c₀ if one of the infinite-dimensional Banach...

On conditions for the boundedness of the Weyl fractional integral on weighted L p spaces

Liliana De Rosa, Alberto de la Torre (2004)

Commentationes Mathematicae Universitatis Carolinae

In this paper we give a sufficient condition on the pair of weights ( w , v ) for the boundedness of the Weyl fractional integral I α + from L p ( v ) into L p ( w ) . Under some restrictions on w and v , this condition is also necessary. Besides, it allows us to show that for any p : 1 p < there exist non-trivial weights w such that I α + is bounded from L p ( w ) into itself, even in the case α > 1 .

On contractive projections in Hardy spaces

Florence Lancien, Beata Randrianantoanina, Eric Ricard (2005)

Studia Mathematica

We prove a conjecture of Wojtaszczyk that for 1 ≤ p < ∞, p ≠ 2, H p ( ) does not admit any norm one projections with dimension of the range finite and greater than 1. This implies in particular that for 1 ≤ p < ∞, p ≠ 2, H p does not admit a Schauder basis with constant one.

On copies of c 0 in the bounded linear operator space

Juan Carlos Ferrando, J. M. Amigó (2000)

Czechoslovak Mathematical Journal

In this note we study some properties concerning certain copies of the classic Banach space c 0 in the Banach space X , Y of all bounded linear operators between a normed space X and a Banach space Y equipped with the norm of the uniform convergence of operators.

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