论文标题
全态函数Banach代数的光谱在多磁型域上
The spectra of Banach algebras of holomorphic functions on polydisk type domains
论文作者
论文摘要
R.M. Aron等。证明了Banach代数$ \ MATHCAL {H}^\ infty（B_ {C_0}）$中的Banach代数$ \ Mathcal $ \ Mathcal $ \ Mathcal $ \ Mathcal中的群集值定理。另一方面，B.J。Cole和T.W. Gamelin表明，$ \ Mathcal {h}^\ infty（\ ell_2 \ cap b_ {c_0}）$在Algebra的意义上是异态异，对$ \ Mathcal {h}^\ infty（b_ {c_0}）$。在这项工作的激励下，我们对一类开放子集$ u $ u $ u $感兴趣，$ \ mathcal {h}^\ infty（u）$是同构对$ \ mathcal {h}^\ infty（b_ {c_0}）$。我们证明，存在带有Schauder基础的任何无限尺寸Banach Space $ X $的Polydisk类型域，以至于$ \ nathcal {h}^\ infty（u）$在$ \ nathcal到$ \ Mathcal {h}^}^\ infty（b_ infty（c_0} $ cole and cam and cam and and and cam）insomemorthic to insomorphic to $ \ Mathcal {H}此外，我们研究了$ \ Mathcal {h}^\ infty（u）$的频谱的分析和代数结构，并表明群集值定理对于$ \ MATHCAL {H}^\ infty（u）$是正确的。
R.M. Aron et al. proved that the Cluster Value Theorem in the infinite dimensional Banach space setting holds for the Banach algebra $\mathcal{H}^\infty (B_{c_0})$. On the other hand, B.J. Cole and T.W. Gamelin showed that $\mathcal{H}^\infty (\ell_2 \cap B_{c_0})$ is isometrically isomorphic to $\mathcal{H}^\infty (B_{c_0})$ in the sense of an algebra. Motivated by this work, we are interested in a class of open subsets $U$ of a Banach space $X$ for which $\mathcal{H}^\infty (U)$ is isometrically isomorphic to $\mathcal{H}^\infty (B_{c_0})$. We prove that there exist polydisk type domains $U$ of any infinite dimensional Banach space $X$ with a Schauder basis such that $\mathcal{H}^\infty (U)$ is isometrically isomorphic to $\mathcal{H}^\infty (B_{c_0})$, which generalizes the result by Cole and Gamelin. Furthermore, we study the analytic and algebraic structure of the spectrum of $\mathcal{H}^\infty (U)$ and show that the Cluster Value Theorem is true for $\mathcal{H}^\infty (U)$.
