QUASI-LOCAL CONJUGACY THEOREMS IN BANACH SPACES

Let f ： U（x0） belong to E → F be a C^1 map and f＇（x0） be the Frechet derivative of f at x0. In local analysis of nonlinear functional analysis, implicit function theorem, inverse function theorem, local surjectivity theorem, local injectivity theorem, and the local conjugacy theorem are well known....

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Vydáno v:	Chinese annals of mathematics. Serie B Ročník 26; číslo 4; s. 551 - 558
Hlavní autoři:	ZHANG, WEIRONG, MA, JIPU
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	01.10.2005
Témata:	Banach空间 Frechet导数准局部共轭理论外部反转 Outer inverse Quasi-local conjugacy theorems Local conjugacy theorem Frechet derivative
ISSN:	0252-9599, 1860-6261
On-line přístup:	Získat plný text
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Popis
Shrnutí:	Let f ： U（x0） belong to E → F be a C^1 map and f＇（x0） be the Frechet derivative of f at x0. In local analysis of nonlinear functional analysis, implicit function theorem, inverse function theorem, local surjectivity theorem, local injectivity theorem, and the local conjugacy theorem are well known. Those theorems are established by using the properties： f＇（x0） is double splitting and R（f＇（x）） ∩ N（T0^＋） = {0} near x0. However, in infinite dimensional Banach spaces, f＇（x0） is not always double splitting （i.e., the generalized inverse of f（x0） does not always exist）, but its bounded outer inverse of f＇（x0） always exists. Only using the C^1 map f and the outer inverse To^# of f（x0）, the authors obtain two quasi-local conjugacy theorems, which imply the local conjugacy theorem if x0 is a locally fine point of f. Hence the quasi-local conjugacy theorems generalize the local conjugacy theorem in Banach spaces.
Bibliografie:	O177.2 Frechet derivative, Quasi-local conjugacy theorems, Outer inverse, Local conjugacy theorem 31-1329/O1
ISSN:	0252-9599 1860-6261
DOI:	10.1142/S0252959905000440