## Linear Operators: Spectral operators |

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Page 2239

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. Since f Xe

is a bounded function , the operator T ' ( f Xe ) is a bounded operator . If x is in E (

ē ) X as well as in E ( e ) X , it

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. Since f Xe

is a bounded function , the operator T ' ( f Xe ) is a bounded operator . If x is in E (

ē ) X as well as in E ( e ) X , it

**follows**from the operational calculus for bounded ...Page 2246

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. Let Pin it

of C. It is clear then that ( ^ I – C ) R ( ) . 2 for x in H and R ( A ) ( A -C ) x = x for x ...

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. Let Pin it

**follows**that R ( a ) is a bounded operator whose range is contained in the domainof C. It is clear then that ( ^ I – C ) R ( ) . 2 for x in H and R ( A ) ( A -C ) x = x for x ...

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Statement ( b ) of our lemma

statement ( a ) of our theorem

were not dense in Lac ( H ) , it would

Corollary ...

Statement ( b ) of our lemma

**follows**at once . If xn € { ac ( H ) and ... Thusstatement ( a ) of our theorem

**follows**. If F is a bounded ... If ( il – H ) - Lac ( H )were not dense in Lac ( H ) , it would

**follow**by the Hahn - Banach theorem ( cf.Corollary ...

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### Contents

SPECTRAL OPERATORS 1937 1941 1945 XV Spectral Operators | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

32 other sections not shown

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### Common terms and phrases

adjoint operator Amer analytic apply arbitrary assumed B-space Banach space belongs Boolean algebra Borel set boundary conditions bounded bounded operator Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension fact finite follows formal formula function given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear operator Math Moreover multiplicity norm perturbation plane positive preceding present problem projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type seen sequence shown shows similar solution spectral measure spectral operator spectrum subset sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero