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| INVERSES OF OPERATORS BETWEEN BANACH SPACES AND LOCAL CONJUGACY THEOREM |
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Citation： |
MA Jipu.INVERSES OF OPERATORS BETWEEN BANACH SPACES AND LOCAL CONJUGACY THEOREM[J].Chinese Annals of Mathematics B,1999,20(1):57~62 |
| Page view： 929
Net amount： 614 |
Authors： |
MA Jipu; |
Foundation： |
National Natural Science Foundation of China and Jiangsu Provincial Natural;
Science Foundation of China |
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| Abstract： |
Let $E$ and $F$ be Banach spaces and $ f $ non-linear $ C^{1} $ map from $E$ into $F$. The main result is Theorem 2.2, in which a connection between local conjugacy problem of $ f $ at $ x_0\in E $ and a local fine property of $ f^{\prime}(x) $ at $ x_0 $(see the Definition 1.1 in this paper) are obtained.
This theorem includes as special cases the two known theorems: the finite rank theorem and Berger's Theorem for
non-linear Fredholm operators. Moreover, the theorem gives rise the further results for some non-linear semi-Fredholm maps and for all non-linear semi-Fredholm maps when $E$ and $F$ are Hilbert spaces. Thus Theorem 2.2 not only just unifies the above known theorems but also really generalizes them. |
Keywords： |
Nonlinear semi-Fredholm maps, Conjugacy problem,
Banach space |
Classification： |
47H |
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