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On automorphisms of the Banach space / c

Piotr Koszmider, Cristóbal Rodríguez-Porras (2016)

Fundamenta Mathematicae

We investigate Banach space automorphisms T : / c / c focusing on the possibility of representing their fragments of the form T B , A : ( A ) / c ( A ) ( B ) / c ( B ) for A,B ⊆ ℕ infinite by means of linear operators from ( A ) into ( B ) , infinite A×B-matrices, continuous maps from B* = βB∖B into A*, or bijections from B to A. This leads to the analysis of general bounded linear operators on / c . We present many examples, introduce and investigate several classes of operators, for some of them we obtain satisfactory representations and for others give...

On Banach spaces C(K) isomorphic to c₀(Γ)

Witold Marciszewski (2003)

Studia Mathematica

We give a characterization of compact spaces K such that the Banach space C(K) is isomorphic to the space c₀(Γ) for some set Γ. As an application we show that there exists an Eberlein compact space K of weight ω ω and with the third derived set K ( 3 ) empty such that the space C(K) is not isomorphic to any c₀(Γ). For this compactum K, the spaces C(K) and c ( ω ω ) are examples of weakly compactly generated (WCG) Banach spaces which are Lipschitz isomorphic but not isomorphic.

On Bell's duality theorem for harmonic functions

Joaquín Motos, Salvador Pérez-Esteva (1999)

Studia Mathematica

Define h ( E ) as the subspace of C ( B ̅ L , E ) consisting of all harmonic functions in B, where B is the ball in the n-dimensional Euclidean space and E is any Banach space. Consider also the space h - ( E * ) consisting of all harmonic E*-valued functions g such that ( 1 - | x | ) m f is bounded for some m>0. Then the dual h ( E * ) is represented by h - ( E * ) through f , g 0 = l i m r 1 ʃ B f ( r x ) , g ( x ) d x , f h - ( E * ) , g h ( E ) . This extends the results of S. Bell in the scalar case.

On BMO-regular couples of lattices of measurable functions

S. V. Kislyakov (2003)

Studia Mathematica

We introduce a new “weak” BMO-regularity condition for couples (X,Y) of lattices of measurable functions on the circle (Definition 3, Section 9), describe it in terms of the lattice X 1 / 2 ( Y ' ) 1 / 2 , and prove that this condition still ensures “good” interpolation for the couple ( X A , Y A ) of the Hardy-type spaces corresponding to X and Y (Theorem 1, Section 9). Also, we present a neat version of Pisier’s approach to interpolation of Hardy-type subspaces (Theorem 2, Section 13). These two main results of the paper are...

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 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 dense ideals in spaces of analytic functions

Mihai Putinar (1994)

Annales de l'institut Fourier

One proves the density of an ideal of analytic functions into the closure of analytic functions in a L p ( μ ) -space, under some geometric conditions on the support of the measure μ and the zero variety of the ideal.

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