标题： 全纯映射及其在自旋因子上的不动点 显示英文标题

标题： Holomorphic mappings and their fixed points on Spin Factors

摘要： 在本文中，我们研究无限维自旋因子的全纯性质。 在具有齐次开单位球的无限维巴拿赫空间中，我们证明自旋因子是自然的异常空间，在其中可以提出这个问题（如20世纪70年代初对希尔伯特空间所证明的）：双全纯自同构$g$的开单位球$B$是否在$\overline B$中有不动点？ 在本文中，对于无限维自旋因子，我们提供了关于$g$的合理条件，使我们能够显式构造位于$\partial B$上的$g$的不动点。 在此过程中，我们还证明了每个自旋因子都具有稠密性。 在另一个方向上，我们关注(紧的)全纯映射$f:B\rightarrow B$，在$B$中没有不动点，并研究迭代序列$(f^n)$。 由于$(f^n)$通常不收敛，我们转而追踪目标集$T(f)$of$f$，即所有$(f^n)_n$的聚点在 B 上比逐点收敛拓扑更细的任何拓扑下的像。 我们证明对于一个自旋因子，$T(f)$位于仅属于$f$的单个双圆盘的边界上。 显示英文摘要

摘要： In this paper we study holomorphic properties of infinite dimensional spin factors. Among the infinite dimensional Banach spaces with homogeneous open unit balls, we show that the spin factors are natural outlier spaces in which to ask the question (as was proved in the early 1970s for Hilbert spaces): Do biholomorphic automorphisms $g$ of the open unit ball $B$ have fixed points in $\overline B$? In this paper, for infinite dimensional spin factors, we provide reasonable conditions on $g$ that allow us to explicitly construct fixed points of $g$ lying on $\partial B$. En route, we also prove that every spin factor has the density property. In another direction, we focus on (compact) holomorphic maps $f:B\rightarrow B$, having no fixed point in $B$ and examine the sequence of iterates $(f^n)$. As $(f^n)$ does not generally converge, we instead trace the target set $T(f)$ of $f$, that is, the images of all accumulation points of $(f^n)_n$, for any topology finer than the topology of pointwise convergence on B. We prove for a spin factor that $T(f)$ lies on the boundary of a single bidisc unique to $f$.