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De la Sen, M.

On a class of self-adjoint compact operators in Hilbert spaces and their relations with their finite-range truncations. (English) Zbl 1437.47005

Abstr. Appl. Anal. 2013, Article ID 890657, 14 p. (2013).
Summary: This paper investigates a class of self-adjoint compact operators in Hilbert spaces related to their truncated versions with finite-dimensional ranges. The comparisons are established in terms of worst-case norm errors of the composite operators generated from iterated computations. Some boundedness properties of the worst-case norms of the errors in their respective fixed points in which they exist are also given. The iterated sequences are expanded in separable Hilbert spaces through the use of numerable orthonormal bases.

MSC:

47A58 Linear operator approximation theory
47B02 Operators on Hilbert spaces (general)
47J25 Iterative procedures involving nonlinear operators
47N70 Applications of operator theory in systems, signals, circuits, and control theory

Keywords:

self-adjoint compact operators in Hilbert spaces; finite-range truncations; worst-case norm errors; iterated computations; boundedness properties; fixed points; iterated sequences; separable Hilbert spaces; numerable orthonormal bases
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\textit{M. De la Sen}, Abstr. Appl. Anal. 2013, Article ID 890657, 14 p. (2013; Zbl 1437.47005)
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References:

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