Sesión Análisis Funcional y ComplejoMonomial bases for holomorphic functions on Banach spaces with an unconditional basis
Thiago Grando
Universidade Estadual do Centro-Oeste, Brasil - Esta dirección de correo electrónico está siendo protegida contra los robots de spam. Necesita tener JavaScript habilitado para poder verlo.
We study monomial Schauder bases in spaces of entire holomorphic functions on complex Banach spaces. Let \(X\) be a complex Banach space admitting an unconditional Schauder basis, and let \(\tau_0\) denote the compact-open topology on \(\mathcal{H}(X)\). We prove that the monomials associated with the basis of \(X\), endowed with the square order in each homogeneous degree and with any compatible ordering, form a Schauder basis of \((\mathcal{H}(X),\tau_0)\). The proof is based on a fundamental system of compact solid subsets of \(X\) and on coordinatewise Fourier projections. These projections yield the estimate \(c_{K,n}\leq n+1\) for the basis constants of the degree-\(n\) monomials on the relevant compact sets, which allows us to apply an abstract criterion for \(S_*\)-absolute decompositions. As consequences, the result applies to several classical and non-classical Banach spaces, including sequence lattices, Lorentz and Orlicz sequence spaces, Schreier-type spaces, and suitable vector-valued sequence spaces.