## Linear Operators: Spectral theory |

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Page 931

The theorem of Wermer [4] cited in the preceding paragraph gives a condition

under which the

again normal. Wermer [5] studied the

...

The theorem of Wermer [4] cited in the preceding paragraph gives a condition

under which the

**restriction**of a normal operator to every invariant subspace isagain normal. Wermer [5] studied the

**restriction**of an operator T to a subspace J...

Page 1218

... every e > 0 there is a Borel set o in R with a(q)< e and such that the

of f to the complement of q is continuous. PRoof. If the

continuous then so is the

measurable ...

... every e > 0 there is a Borel set o in R with a(q)< e and such that the

**restriction**of f to the complement of q is continuous. PRoof. If the

**restrictions**flo, g|ó arecontinuous then so is the

**restriction**(xf-i-Bg)|o n 6 and thus the class ofmeasurable ...

Page 1239

Conversely, let T be a self adjoint extension of T. Then by Lemma 26, T, is the

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 the

**restriction**of To to a subspace Q3 of Q(T*) determined by a symmetric family oflinearly independent boundary conditions B, (a) = 0, i = 1,..., k, and we have only

to ...

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

34 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

additive Akad algebra Amer analytic applied assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complete Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function function f given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math measure multiplicity neighborhood norm obtained partial positive preceding present problem projection PRoof properties prove range regular remark representation respectively restriction result satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero