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Displaying similar documents to “The Fredholm theory of integral equations for special types of compact operators on a separable Hilbert space”

On an estimate for the norm of a function of a quasihermitian operator

M. Gil (1992)

Studia Mathematica

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Let A be a closed linear operator acting in a separable Hilbert space. Denote by co(A) the closed convex hull of the spectrum of A. An estimate for the norm of f(A) is obtained under the following conditions: f is a holomorphic function in a neighbourhood of co(A), and for some integer p the operator A p - ( A * ) p is Hilbert-Schmidt. The estimate improves one by I. Gelfand and G. Shilov.

Perturbation theory relative to a Banach algebra of operators

Bruce Barnes (1993)

Studia Mathematica

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Let ℬ be a Banach algebra of bounded linear operators on a Banach space X. Let S be a closed linear operator in X, and let R be a linear operator in X. In this paper the spectral and Fredholm theory relative to ℬ of the perturbed operator S + R is developed. In particular, the situation where R is S-inessential relative to ℬ is studied. Several examples are given to illustrate the usefulness of these concepts.

Compact AC-operators

Ian Doust, Byron Walden (1996)

Studia Mathematica

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We prove that compact AC-operators have a representation as a combination of disjoint projections which mirrors that for compact normal operators. We also show that unlike arbitrary AC-operators, compact AC-operators admit a unique splitting into real and imaginary parts, and that these parts must necessarily be compact.