Factorization of fredholm operators on analytic functions
نویسندگان
چکیده
منابع مشابه
Composition operators acting on weighted Hilbert spaces of analytic functions
In this paper, we considered composition operators on weighted Hilbert spaces of analytic functions and observed that a formula for the essential norm, gives a Hilbert-Schmidt characterization and characterizes the membership in Schatten-class for these operators. Also, closed range composition operators are investigated.
متن کاملcomposition operators acting on weighted hilbert spaces of analytic functions
in this paper, we considered composition operators on weighted hilbert spaces of analytic functions and observed that a formula for the essential norm, gives a hilbert-schmidt characterization and characterizes the membership in schatten-class for these operators. also, closed range composition operators are investigated.
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A bounded operator T on a separable, complex Hilbert space is said to be odd symmetric if IT I = T where I is a real unitary satisfying I = −1 and T t denotes the transpose of T . It is proved that such an operator can always be factorized as T = IAIA with some operator A. This generalizes a result of Hua and Siegel for matrices. As application it is proved that the set of odd symmetric Fredhol...
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(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...
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An interval method for finding a polynomial factor of an analytic function f(z) is proposed. By using a Samelson-like method recursively, we obtain a sequence of polynomials that converges to a factor p∗(z) of f(z) if an initial approximate factor p(z) is sufficiently close to p∗(z). This method includes some well known iterative formulae, and has a close relation to a rational approximation. A...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 1978
ISSN: 0022-1236
DOI: 10.1016/0022-1236(78)90036-8