Starlike, convex, close-to-convex, spiral-like, and Φ-like maps in a commutative Banach algebra with identity
Starlike, convex, close-to-convex, spiral-like, and Φ-like maps in a commutative Banach algebra with identity
复制标题
具有恒等式的交换巴纳赫代数中的星形、凸形、近凸形、螺旋形和 Φ 形映射
DOI：
10.1090/s0002-9947-1979-0530050-x
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发表时间：
1979
影响因子：
1.3
通讯作者：
T. J. Suffridge
中科院分区：
文献类型：
--
作者：
L. F. Heath;T. J. Suffridge
设C(X)是紧化t2空间X上的连续函数空间其中Jf的每个点都是g。如果F: B -»C(X)是B ={/1 || /1| < 1}到DF(0) = I的凸域上的生物全纯映射（即F和F ~ '是Frechet可微的），则F是Lorch解析映射(即对于某些ai C（X)， DF(fXg) = afg）。设R是具有恒等式的交换巴拿赫代数，使得R在CC3H中的Gelfand同态是等距的。星形、凸形、近凸形、螺旋形和$形函数定义在B = {x£* I 11*11 < 1} for ？-解析函数在B中，它们与关联的复值全纯函数在A中= {z e C| |z| < 1)。
Let C(X) be the space of continuous functions on a compact T2-space X where each point of Jf is a Gs. If F: B -» C(X) is a biholomorphic (in the sense that F and F ~ ' are Frechet differentiable) map of B = {/1 || /1| < 1} onto a convex domain with DF(0) = I, then F is Lorch analytic (i.e., DF(fXg) = afg for some ai e C(X)). Let R be a commutative Banach algebra with identity such that the Gelfand homomorphism of R into CC3H) is an isometry. Starlike, convex, close-to-convex, spirallike and $-like functions are defined in B = {x £ * I 11*11 < 1} for ?-analytic functions in B and they are related to associated complex-valued holomorphic functions in A = {z e C| |z| < 1).