Resumen de Basis in the big disk algebra and in the corresponding Hardy-space
F. Lancien
t is well known that the disk algebra $A(\mathbb{T})$ has a basis [1] and that $H^1(\mathbb{T})$ has an unconditional basis [9]. Recently W. Lusky gave new proofs of these results using the commuting bounded approximation property ([7] and [8]).\newline With similar methods we prove the existence of a basis in the so called "big disk algebra" $\mathcal{A}(\mathbb{T}^N)$, the space of continuous functions on the multidimensional torus $\mathbb{T}^N$ which are "analytic" with respect to the lexicographic order on the dual group $\mathbb{Z}^N$ and in the space $\mathcal{H}^1(\mathbb{T}^N)$, the analog for $L^1$ functions on $\mathbb{T}^N$.
