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We discuss some open problems in the Geometry of Banach spaces having Ramsey-theoretic flavor. The problems are exposed together with well known results related to them.
We study Banach spaces of harmonic functions on open sets of $$\mathbb R ^{N}$$ or $$\mathbb C ^N$$ endowed with weighted supremum norms. We investigate the harmonic associated weight defined naturally as the analogue of the holomorphic associated weight introduced by Bierstedt, Bonet, and Taskinen and we compare them. We study composition operators with holomorphic symbol between weighted...
Given two balanced compact subsets K and L of two Banach spaces X and Y respectively such that every continuous m-homogeneous polynomial on $$X^{**}$$ X ∗ ∗ and on $$Y^{**}$$ Y ∗ ∗ is approximable, for all $$m\in \mathbb {N}$$ m ∈ N , we characterize when the algebras of holomorphic germs $$\mathcal {H}(K)$$ H ( K ) and $$\mathcal {H}(L)$$ ...
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