# compact operator

(redirected from Completely continuous Operator)

## compact operator

[¦käm‚pakt ′äp·ə‚rād·ər]
(mathematics)
A linear transformation from one normed vector space to another, with the property that the image of every bounded set has a compact closure.
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Besides, using the Arzela Ascoli theorem and the standard arguments, one can easily show that T : p [right arrow] p is completely continuous operator.
1]) [right arrow] K is completely continuous operator such that either
Proof: Let T be the cone preserving, completely continuous operator defined as in (2.
Keywords: Time scale, delta and nabla derivatives and integrals, Green's function, completely continuous operator, eigenfunction expansion.
Next in Section 3 it is shown, by using the Hilbert-Schmidt theorem on symmetric completely continuous operators, that the eigenvalue problem (1.
Then A : K [right arrow] K is a completely continuous operator.
rho]] [intersection] P [right arrow] P be a completely continuous operator, i(A,[B.
1]) [right arrow] K is completely continuous operator such that either (i) [parallel]Au[parallel] [less than or equal to] [parallel]u[parallel], u [member of] k [intersection] [partial derivative][[OMEGA].
Representing completely continuous operators through weakly [infinity]-compact operators.
Moshtaghioun introduced the class of limited completely continuous operators, and characterized this class of operators and studied some of its properties in [12].
offer more than 100 exercise while covering linear spaces, topological spaces, metric spaces, normed linear spaces and Banach spaces, inner product spaces and Hilbert spaces, linear functionals, types of convergence in function space, reproducing kernel Hilbert spaces, order relations in function spaces, operators in function space, completely continuous operators, approximation methods for linear operator equations, interval methods for operator equations, contraction mappings and iterative methods, Newton's method in Banach spaces, variants of Newton's methods, and homotopy and continuation methods and a hybrid method for a free-boundary problem.
Next, we give an existence result based upon the following form of fixed point theorem applied to completely continuous operators [20].

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