## 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 A , € C , , , A , € C , , , Az € Cr , where ri...

Page 1226

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

...

Page 1733

( C ) , it follows that 4 - 1110S - fla is uniformly bounded in 1 , from which the

present

enables us to use the method of proof of Theorem 2 in the neighborhood of the

boundary of a ...

( C ) , it follows that 4 - 1110S - fla is uniformly bounded in 1 , from which the

present

**lemma**follows , as has been shown above . Q . E . D .**Lemma**18enables us to use the method of proof of Theorem 2 in the neighborhood of the

boundary of a ...

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### Contents

IX | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Compact Groups | 945 |

Copyright | |

46 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 operator algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently consider constant contains continuous converges Corollary corresponding defined Definition denote dense derivatives determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function 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 satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero