## Linear Operators, Part 2 |

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Page 890

... then the function E is a resolution of the identity for T and the operational calculus is given by the

... then the function E is a resolution of the identity for T and the operational calculus is given by the

**formula**( vi ) ( T ) = Soxxy : ( 2 ) E ( 11 ) ...Page 1089

This

This

**formula**may be written ( un ( T ) ) 2 = min 91 , ... , Pin max 17912 19 = 1 ( 4,8 , ) = ... ( P.Pn ) = 0 Since 1T9 | 2 = ( T9 , Tp ) ( T * T9,9 ) ...Page 1363

basis for this

basis for this

**formula**is found in Theorem XII.2.10 which asserts that the projection in the resolution of the identity for T corresponding to ( 12 ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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additive Akad algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex 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 matrix measure multiplicity neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result Russian satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero