On the Fredholm alternative for nonlinear operators
نویسندگان
چکیده
منابع مشابه
On the Fredholm Alternative for Nonlinear Operators
Let X be a locally convex topological vector space, Y a real Banach space, ƒ a mapping (in general, nonlinear) of X into Y. In several recent papers ([5], [ó], [7]), Pohozaev has studied the concept of normal solvability or the Fredholm alternative for mappings ƒ of class C. If Ax=f'x' is the continuous linear mapping of X into Y which is the derivative of ƒ a t the point x of X, A* the adjoint...
متن کاملNotes on Fredholm operators
(2) If K ∈ B(X) is compact, then for all λ ∈ C \ {0}, K − λ1 is Fredholm with index zero. (3) The shift operator S± ∈ B(`p) for 1 ≤ p ≤ ∞ defined by (S±x)n = xn±1 is Fredholm with index ±1. (4) If X,Y are finite dimensional and T ∈ B(X,Y ), then by the Rank-Nullity Theorem, ind(T ) = dim(X)− dim(Y ). Lemma 3. Suppose E,F ⊆ X are closed subspaces with F finite dimensional. (1) The subspace E + F...
متن کاملA Simple Proof of the Fredholm Alternative and a Characterization of the Fredholm Operators
Let A be a linear bounded operator in a Hilbert space H, N(A) and R(A) its null-space and range, and A∗ its adjoint. The operator A is called Fredholm iff dim N(A) = dim N(A∗) := n < ∞ and R(A) and R(A∗) are closed subspaces of H. A simple and short proof is given of the following known result: A is Fredholm iff A = B + F , where B is an isomorphism and F is a finite-rank operator. The proof co...
متن کاملOn the space of Fredholm operators
We compare various topologies on the space of (possibly unbounded) Fredholm selfadjoint operators and explain their K-theoretic relevance.∗ Introduction The work of Atiyah and Singer on the index of elliptic operators on manifolds has singled out the role of the space of bounded Fredholm operators in topology. It is a classifying space for a very useful functor, the topological K-theory. This m...
متن کاملOn the Fredholm Alternative for the Fucيk Spectrum
and Applied Analysis 3 which is extended to 0, πp and then 0, 2πp by symmetry, and then to all of as a 2πp periodic function. See, for example, 3, 4 . Note that, we have u1 > 0 in 0, T , and u1 is a nontrivial solution of 1.5 for α, β λ1, β , with arbitrary β ∈ . Obviously, this implies that λ1 × ⊂ Σp. Similarly, × λ1 ⊂ Σp with a corresponding nontrivial solution, −u1 < 0 in 0, T . It is helpfu...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1970
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1970-12527-7