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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

Chapter:
(p.93) 3 Unbounded Linear Operators
Source:
Spectral Theory and Differential Operators
Author(s):

D. E. Edmunds

W. D. Evans

Publisher:
Oxford University Press
DOI:10.1093/oso/9780198812050.003.0003

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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