compact operator

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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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N is said to be completely continuous if N(B) is relatively compact for every B [member of] [P.
3) hold, then the operator C is completely continuous on M.
By a standard argument, it is easy to see that A : P [right arrow] P is completely continuous.
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.
An operator is called completely continuous if it is continuous and maps bounded sets into pre-compact sets.
In one project, Peaslee and his team of researchers are developing a new process that is completely continuous from start to finish, unlike many current steelmaking processes.
If J additionally is completely continuous then J has a countable set of eigenvalues which can be characterized as minmax and maxmin values of the Rayleigh quotient by the principles of Poincare and of Courant, Fischer and Weyl.
P([gamma], c)] is completely continuous and there exist nonnegative numbers h, a, k, b, with 0 < a < b such that
Keywords: Time scale, delta and nabla derivatives and integrals, Green's function, completely continuous operator, eigenfunction expansion.
Suppose there exists a completely continuous operator [PHI]: /P([gamma], c) [right arrow] P and 0 < a < b < c such that
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].

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