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Generalized Fredholm operators
Archiv der Mathematik, 1985The classical Fredholm theory in Banach spaces studies normally solvable operators with null space or conull space in F, the ideal of all finite dimensional Banach spaces. The aim of this paper is to study normally solvable operators with null space or conull space in an arbitrary space ideal A.
Alvarez, Teresa, Onieva, Victor M.
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Journal of Mathematical Sciences
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Operator Estimates for Fredholm Modules
Canadian Journal of Mathematics, 2000AbstractWe study estimates of the typewhere φ(t) = t(1 + t2)−1/2, D0 = D0* is an unbounded linear operator affiliated with a semifinite von Neumann algebra , D − D0 is a bounded self-adjoint linear operator from and , where E(, τ) is a symmetric operator space associated with .
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1987
In this chapter a connection is established between the Fredholmness of the operator A = [A mk ] m,k=1 n in the Cartesian product E n = E × ... × E of n copies of a Banach space E and the Fredholmness of its determinant det[A mk ] in E. Conditions are given under which the indices of these two operators coincide.
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In this chapter a connection is established between the Fredholmness of the operator A = [A mk ] m,k=1 n in the Cartesian product E n = E × ... × E of n copies of a Banach space E and the Fredholmness of its determinant det[A mk ] in E. Conditions are given under which the indices of these two operators coincide.
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2011
The theory of linear Fredholm operators will be used in this chapter to study onlinear elliptic problems. Nonlinear operators are called Fredholm operators if the corresponding linearized operators satisfy this property.
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The theory of linear Fredholm operators will be used in this chapter to study onlinear elliptic problems. Nonlinear operators are called Fredholm operators if the corresponding linearized operators satisfy this property.
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2011
The theory of elliptic problems is essentially based on their Fredholm property which determines solvability conditions and a well-defined index. The Fredholm property and index are preserved under small perturbations of the operators. The situation is quite different if the Fredholm property is not satisfied. A general theory of such problems does not
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The theory of elliptic problems is essentially based on their Fredholm property which determines solvability conditions and a well-defined index. The Fredholm property and index are preserved under small perturbations of the operators. The situation is quite different if the Fredholm property is not satisfied. A general theory of such problems does not
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Fredholm weighted composition operators
Integral Equations and Operator Theory, 1993For a compact Hausdorff space \(X\) and some functional space \(F(X)\) on \(X\) a weighted composition operator is defined as \(uC_ \varphi f(x):=u(x)f(\varphi (x))\), where \(\varphi: X\to X\) is an automorphism. The author obtains criteria for the operator \(uC_ \varphi: C(X)\to C(X)\) to be a Fredholm operator and finds that in the case when \(X ...
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Compact and Fredholm Operators
1993The operators in infinite dimensional spaces closest to operators in finite dimensional spaces are the compact operators, which will now be studied systematically. A large number of examples of compact operators are given in the exercises.
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