Basis in the big disk algebra and in the corresponding Hardy-space

• Autores: F. Lancien
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 48, Fasc. 3, 1997, págs. 235-242
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • 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 $\mathbb{T}^N$.

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