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Spectral Theory and Special Classes of Operators

In: Elements of Hilbert Spaces and Operator Theory

Author

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  • Harkrishan Lal Vasudeva

    (Indian Institute of Science Education and Research)

Abstract

Spectrum of an operator is the key to the understanding of the operator. Properties of the spectrum and its splitting into different parts (point spectrum, continuous spectrum, residual spectrum) in relation to normal, self-adjoint, unitaries and isometries have been discussed. Notion of numerical range and its connection with spectral radius have been explored. Spectral mapping theorems and spectral theorems for self-adjoint and normal operators form part of this Chapter; so does invariant subspace problem with special reference to Volterra operator. Unbounded operators are also briefly discussed.

Suggested Citation

  • Harkrishan Lal Vasudeva, 2017. "Spectral Theory and Special Classes of Operators," Springer Books, in: Elements of Hilbert Spaces and Operator Theory, chapter 0, pages 233-371, Springer.
    • Handle: RePEc:spr:sprchp:978-981-10-3020-8_4
    DOI: 10.1007/978-981-10-3020-8_4
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