## Linear Operators: Spectral theory |

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Page 1188

Q.E.D. The Hilbert space adjoint To" of a bounded operator T in Hilbert space has

been

necessarily bounded and this concept is formulated in the following

Q.E.D. The Hilbert space adjoint To" of a bounded operator T in Hilbert space has

been

**defined**by the identity (Tal, ... space adjoint of an operator which is notnecessarily bounded and this concept is formulated in the following

**definition**.Page 1196

bounded Borel functions into an algebra of normal operators in Hilbert space and

thus the above formula

identity for the self adjoint operator T and let f be a complex Borel function

bounded Borel functions into an algebra of normal operators in Hilbert space and

thus the above formula

**defines**an operational ... Let E be the resolution of theidentity for the self adjoint operator T and let f be a complex Borel function

**defined**...Page 1645

92 ôa by This is an operator densely

... In order for such an answer to make sense, it is desirable that we should be

able to

92 ôa by This is an operator densely

**defined**in L2(E*), but not a closed operator.... In order for such an answer to make sense, it is desirable that we should be

able to

**define**6, 8, for every function, differentiable or not, and irrespective of ...### What people are saying - Write a review

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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