## Linear Operators: Spectral theory |

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Page 1144

31 , we obtain the two following corollaries , which generalize Corollaries 9 . 30

and 9 . 31 . 16 Corollary . Let the arcs Yı , . . . , ys be chosen as in the preceding

theorem and suppose that as a tends to zero along any of these arcs the

31 , we obtain the two following corollaries , which generalize Corollaries 9 . 30

and 9 . 31 . 16 Corollary . Let the arcs Yı , . . . , ys be chosen as in the preceding

theorem and suppose that as a tends to zero along any of these arcs the

**resolvent**...Page 1187

Just as in the case of a bounded operator the

is defined to be the set of all complex numbers a such that ( 21 – T ) - 1 exists as

an everywhere defined bounded operator . For 2 in p ( T ) the symbol R ( 2 ; T ) ...

Just as in the case of a bounded operator the

**resolvent**set p ( T ) of an operator Tis defined to be the set of all complex numbers a such that ( 21 – T ) - 1 exists as

an everywhere defined bounded operator . For 2 in p ( T ) the symbol R ( 2 ; T ) ...

Page 1422

Thus , from ( †t ] is follows that - i is in the

real number such that the whole interval [ - i , - Moi ) of the negative imaginary

axis is in the

Thus , from ( †t ] is follows that - i is in the

**resolvent**set of S . Let Mo be the largestreal number such that the whole interval [ - i , - Moi ) of the negative imaginary

axis is in the

**resolvent**set of S . Since , by Lemma XII . 1 . 3 , the**resolvent**set is ...### 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