## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 61

Page 1099

... matrix may be approximated arbitrarily closely by non -

sufficient to consider the case in which T is non -

is also non -

...

... matrix may be approximated arbitrarily closely by non -

**singular**matrices , it issufficient to consider the case in which T is non -

**singular**. Then A = ( TT * ) 1 / 2is also non -

**singular**and if U = A - 17 , UU * = A - 1 A2 A - 1 = 1 , then U is unitary...

Page 1184

X , V€ A lx - yle These B - spaces have been studied extensively in connection

with the theory of

CalderónZygmund type may be shown under suitable hypotheses to map

functions satisfying a ...

X , V€ A lx - yle These B - spaces have been studied extensively in connection

with the theory of

**singular**integrals .**Singular**integrals of Hilbert -CalderónZygmund type may be shown under suitable hypotheses to map

functions satisfying a ...

Page 1919

7 ( 136 )

258 ) , IV . 5 . 3 ( 259 ) , IV . 6 . 2 – 3 ( 262 – 264 ) , IV . 8 . 16 ( 296 ) definitions , (

160 - 162 ) , IV . 2 . 15 – 17 ( 240 ) , IV . 6 . 1 ( 261 ) remarks on , ( 389 - 390 )

study ...

7 ( 136 )

**singular**, III . 4 . 12 ( 131 ) spaces of , as conjugate spaces , IV . 5 . 1 (258 ) , IV . 5 . 3 ( 259 ) , IV . 6 . 2 – 3 ( 262 – 264 ) , IV . 8 . 16 ( 296 ) definitions , (

160 - 162 ) , IV . 2 . 15 – 17 ( 240 ) , IV . 6 . 1 ( 261 ) remarks on , ( 389 - 390 )

study ...

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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