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Positive bases in ordered subspaces with the Riesz decomposition property

Vasilios Katsikis, Ioannis A. Polyrakis (2006)

Studia Mathematica

In this article we suppose that E is an ordered Banach space whose positive cone is defined by a countable family ℱ = f i | i ∈ ℕ of positive continuous linear functionals on E, i.e. E₊ = x ∈ E | f i ( x ) ≥ 0 for each i, and we study the existence of positive (Schauder) bases in ordered subspaces X of E with the Riesz decomposition property. We consider the elements x of E as sequences x = ( f i ( x ) ) and we develop a process of successive decompositions of a quasi-interior point of X₊ which at each step gives elements with smaller support....

Preduals of Sobolev-Campanato spaces

Konrad Gröger, Lutz Recke (2001)

Mathematica Bohemica

We present definitions of Banach spaces predual to Campanato spaces and Sobolev-Campanato spaces, respectively, and we announce some results on embeddings and isomorphisms between these spaces. Detailed proofs will appear in our paper in Math. Nachr.

Product spaces generated by bilinear maps and duality

Enrique A. Sánchez Pérez (2015)

Czechoslovak Mathematical Journal

In this paper we analyse a definition of a product of Banach spaces that is naturally associated by duality with a space of operators that can be considered as a generalization of the notion of space of multiplication operators. This dual relation allows to understand several constructions coming from different fields of functional analysis that can be seen as instances of the abstract one when a particular product is considered. Some relevant examples and applications are shown, regarding pointwise...

Products of Lipschitz-free spaces and applications

Pedro Levit Kaufmann (2015)

Studia Mathematica

We show that, given a Banach space X, the Lipschitz-free space over X, denoted by ℱ(X), is isomorphic to ( ∑ n = 1 ∞ ℱ ( X ) ) ℓ ₁ . Some applications are presented, including a nonlinear version of Pełczyński’s decomposition method for Lipschitz-free spaces and the identification up to isomorphism between ℱ(ℝⁿ) and the Lipschitz-free space over any compact metric space which is locally bi-Lipschitz embeddable into ℝⁿ and which contains a subset that is Lipschitz equivalent to the unit ball of ℝⁿ. We also show that ℱ(M)...

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