论文标题
非对称规则空间的分析函数代数的同态
Homomorphisms on algebras of analytic functions on non-symmetrically regular spaces
论文作者
论文摘要
我们研究了Banach空间上有限类型的分析函数代数的同态。当域空间缺乏对称的规律性时，我们表明，在光谱的每一个纤维中，都有评估（在较高的双重）中与第二对偶中的评估不一致。我们还考虑了评估之间的卷积的交换性。我们表明，在某些Banach Spaces $ x $（例如，$ x = \ ell_1 $）中，唯一与$ x''$其他所有评估的通勤评估是$ x $中的那些。最后，我们建立条件，以确保对称多线性操作员的规范扩展（在非对称的规则空间上）的对称性，并介绍一些应用。
We study homomorphisms on the algebra of analytic functions of bounded type on a Banach space. When the domain space lacks symmetric regularity, we show that in every fiber of the spectrum there are evaluations (in higher duals) which do not coincide with evaluations in the second dual. We also consider the commutativity of convolutions between evaluations. We show that in some Banach spaces $X$ (for example, $X=\ell_1$) the only evaluations that commute with every other evaluation in $X''$ are those in $X$. Finally, we establish conditions ensuring the symmetry of the canonical extension of a symmetric multilinear operator (on a non-symmetrically regular space) and present some applications.
