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On a Class of Self‐Adjoint Compact Operators in Hilbert Spaces and Their Relations with Their Finite‐Range Truncations

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  • M. De la Sen

Abstract

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.

Suggested Citation

  • M. De la Sen, 2013. "On a Class of Self‐Adjoint Compact Operators in Hilbert Spaces and Their Relations with Their Finite‐Range Truncations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:890657
    DOI: 10.1155/2013/890657
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    References listed on IDEAS

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    1. M. De la Sen, 2012. "Fixed and Best Proximity Points of Cyclic Jointly Accretive and Contractive Self‐Mappings," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    2. S. A. Mohiuddine & Abdullah Alotaibi, 2013. "Some Spaces of Double Sequences Obtained through Invariant Mean and Related Concepts," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-11, April.
    3. M. De la Sen, 2012. "Fixed and Best Proximity Points of Cyclic Jointly Accretive and Contractive Self-Mappings," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-29, April.
    4. Chi-Ming Chen, 2012. "Common Fixed‐Point Theorems in Complete Generalized Metric Spaces," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    5. S. A. Mohiuddine & Abdullah Alotaibi, 2013. "Some Spaces of Double Sequences Obtained through Invariant Mean and Related Concepts," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    6. Chi-Ming Chen, 2012. "Common Fixed-Point Theorems in Complete Generalized Metric Spaces," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-14, May.
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