## Linear Operators: Spectral theory |

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Page 1105

Nelson Dunford, Jacob T. Schwartz. linear . We have tr ( T ) = fr ( T ) , where tr ( T )

is the expression of

inequalities of

...

Nelson Dunford, Jacob T. Schwartz. linear . We have tr ( T ) = fr ( T ) , where tr ( T )

is the expression of

**Lemma**13 ( b ) . We now pause to sharpen another of theinequalities of

**Lemma**9 . 20**Lemma**. Let 4 , € C , , , A , EC , , , Az € C , , where ri...

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Proof . Part ( a ) follows immediately from

immediately from part ( a ) and

b ) that any symmetric operator with dense domain has a unique minimal closed

...

Proof . Part ( a ) follows immediately from

**Lemma**5 ( b ) , and part ( b ) followsimmediately from part ( a ) and

**Lemma**5 ( c ) . Q . E . D . It follows from**Lemma**6 (b ) that any symmetric operator with dense domain has a unique minimal closed

...

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Q . E . D .

neighborhood of the boundary of a domain with smooth boundary . This is carried

out in the next two

Q . E . D .

**Lemma**18 enables us to use the method of proof of Theorem 2 in theneighborhood of the boundary of a domain with smooth boundary . This is carried

out in the next two

**lemmas**. 19**LEMMA**. Let o be an elliptic formal partial ...### What people are saying - Write a review

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### Contents

IX | 859 |

extensive presentation of applications of the spectral theorem | 911 |

Miscellaneous Applications | 937 |

Copyright | |

20 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 adjoint adjoint operator algebra analytic assume B-algebra basis belongs Borel set boundary conditions boundary values bounded called clear closed closure coefficients commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension fact finite follows formal differential operator formula function function f give given Hence Hilbert space ideal identity independent indices inequality integral interval isometric isomorphism Lemma linear mapping matrix measure multiplicity neighborhood norm normal operator obtained positive preceding present projection proof properties prove range regular representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique unit vanishes vector zero