## Linear Operators: Spectral theory |

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Page 1239

Conversely, let T be a self adjoint

restriction of To to a subspace Q3 of Q(T*) determined by a symmetric family of

linearly independent boundary conditions B, (a) = 0, i = 1,..., k, and we have only

to ...

Conversely, let T be a self adjoint

**extension**of T. Then by Lemma 26, T, is therestriction of To to a subspace Q3 of Q(T*) determined by a symmetric family of

linearly independent boundary conditions B, (a) = 0, i = 1,..., k, and we have only

to ...

Page 1261

23 If an operator T has a closed linear

linear

is called the closure of T. (a) There exists a densely defined operator with no

closed ...

23 If an operator T has a closed linear

**extension**there exists a unique closedlinear

**extension**T such that if T is any closed linear**extension**of T then TC T1. Tis called the closure of T. (a) There exists a densely defined operator with no

closed ...

Page 1397

Q.E.D. It follows from Theorem 5 and Corollary 4 that the set of nonisolated points

of the spectrum of a self adjoint

particular

...

Q.E.D. It follows from Theorem 5 and Corollary 4 that the set of nonisolated points

of the spectrum of a self adjoint

**extension**T of To(r) is independent of theparticular

**extension**chosen, i.e., is independent of the particular set of boundary...

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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