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.
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Notes
- 1.
Note that the same theorem had made it possible earlier to divide the complement of the point spectrum into two disjoint parts.
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Vasudeva, H.L. (2017). Spectral Theory and Special Classes of Operators. In: Elements of Hilbert Spaces and Operator Theory. Springer, Singapore. https://doi.org/10.1007/978-981-10-3020-8_4
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DOI: https://doi.org/10.1007/978-981-10-3020-8_4
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Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-3019-2
Online ISBN: 978-981-10-3020-8
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