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Spectral Theory and Differential Operators$
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David Edmunds and Des Evans

Print publication date: 2018

Print ISBN-13: 9780198812050

Published to Oxford Scholarship Online: September 2018

DOI: 10.1093/oso/9780198812050.001.0001

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Unbounded Linear Operators

Unbounded Linear Operators

(p.93) 3 Unbounded Linear Operators
Spectral Theory and Differential Operators

D. E. Edmunds

W. D. Evans

Oxford University Press

This chapter is concerned with closable and closed operators in Hilbert spaces, especially with the special classes of symmetric, J-symmetric, accretive and sectorial operators. The Stone–von Neumann theory of extensions of symmetric operators is treated as a special case of results for compatible adjoint pairs of closed operators. Also discussed in detail is the stability of closedness and self-adjointness under perturbations. The abstract results are applied to operators defined by second-order differential expressions, and Sims’ generalization of the Weyl limit-point, limit-circle characterization for symmetric expressions to J-symmetric expressions is proved.

Keywords:   closable and closed operators, numerical range, field of regularity, stability, compatible adjoint pair

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