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On coincidence of Pettis and McShane integrability

Marián J. Fabián (2015)

Czechoslovak Mathematical Journal

R. Deville and J. Rodríguez proved that, for every Hilbert generated space X , every Pettis integrable function f : [ 0 , 1 ] X is McShane integrable. R. Avilés, G. Plebanek, and J. Rodríguez constructed a weakly compactly generated Banach space X and a scalarly null (hence Pettis integrable) function from [ 0 , 1 ] into X , which was not McShane integrable. We study here the mechanism behind the McShane integrability of scalarly negligible functions from [ 0 , 1 ] (mostly) into C ( K ) spaces. We focus in more detail on the behavior...

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 complex interpolation and spectral continuity

Karen Saxe (1998)

Studia Mathematica

Let [ X 0 , X 1 ] t , 0 ≤ t ≤ 1, be Banach spaces obtained via complex interpolation. With suitable hypotheses, linear operators T that act boundedly on both X 0 and X 1 will act boundedly on each [ X 0 , X 1 ] t . Let T t denote such an operator when considered on [ X 0 , X 1 ] t , and σ ( T t ) denote its spectrum. We are motivated by the question of whether or not the map t σ ( T t ) is continuous on (0,1); this question remains open. In this paper, we study continuity of two related maps: t ( σ ( T t ) ) (polynomially convex hull) and t e ( σ ( T t ) ) (boundary of the polynomially convex...

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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