اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدA generalized version of the Earle-Hamilton fixed point theorem for the Hilbert ball
63
0
0.0
(
0
)
تأليف
David Shoikhet
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Let $D$ be a bounded domain in a complex Banach space. According to the Earle-Hamilton fixed point theorem, if a holomorphic mapping $F : D mapsto D$ maps $D$ strictly into itself, then it has a unique fixed point and its iterates converge to this fixed point locally uniformly. Now let $mathcal{B}$ be the open unit ball in a complex Hilbert space and let $F : mathcal{B} mapsto mathcal{B}$ be holomorphic. We show that a similar conclusion holds even if the image $F(mathcal{B})$ is not strictly inside $mathcal{B}$, but is contained in a horosphere internally tangent to the boundary of $mathcal{B}$. This geometric condition is equivalent to the fact that $F$ is asymptotically strongly nonexpansive with respect to the hyperbolic metric in $mathcal{B}$.
قيم البحث
اقرأ أيضاً
We present a rigidity property of holomorphic generators on the open unit ball $mathbb{B}$ of a Hilbert space $H$. Namely, if $finHol (mathbb{B},H)$ is the generator of a one-parameter continuous semigroup ${F_t}_{tgeq 0}$ on $mathbb{B}$ such that fo
r some boundary point $tauin partialmathbb{B}$, the admissible limit $K$-$limlimits_{ztotau}frac{f(x)}{|x-tau|^{3}}=0$, then $f$ vanishes identically on $mathbb{B}$.
Poincares last geometric theorem (Poincare-Birkhoff Theorem) states that any area-preserving twist map of annulus has at least two fixed points. We replace the area-preserving condition with a weaker intersection property, which states that any essen
tial simple closed curve intersects its image under $f$ at least at one point. The conclusion is that any such map has at least one fixed point. Besides providing a new proof to Poincares geometric theorem, our result also has some applications to reversible systems.
We consider constrained Horn clause solving from the more general point of view of solving formula equations. Constrained Horn clauses correspond to the subclass of Horn formula equations. We state and prove a fixed-point theorem for Horn formula equ
ations which is based on expressing the fixed-point computation of a minimal model of a set of Horn clauses on the object level as a formula in first-order logic with a least fixed point operator. We describe several corollaries of this fixed-point theorem, in particular concerning the logical foundations of program verification, and sketch how to generalise it to incorporate abstract interpretations.
We obtain an extended Reich fixed point theorem for the setting of generalized cone rectangular metric spaces without assuming the normality of the underlying cone. Our work is a generalization of the main result in cite{AAB} and cite{JS}.
This note is devoted to two classical theorems: the open mapping theorem for analytic functions (OMT) and the fundamental theorem of algebra (FTA). We present a new proof of the first theorem, and then derive the second one by a simple topological ar
gument. The proof is elementary in nature and does not use any kind of integration (neither complex nor real). In addition, it is also independent of the fact that the roots of an analytic function are isolated. The proof is based on either the Banach or Brouwer fixed point theorems. In particular, this shows that one can obtain a proof of the FTA (albeit indirect) which is based on the Brouwer fixed point theorem, an aim which was not reached in the past and later the possibility to achieve it was questioned. We close this note with a simple generalization of the FTA. A short review of certain issues related to the OMT and the FTA is also included.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
