## Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |

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Results 1-3 of 88

Page 2203

Let e be an open

and let z > 0 . Then , because of the regularity of xA ( • ) x * , there is a closed

with ...

Let e be an open

**subset**of 1 , let x and 2 * be elements of X , X * , respectively ,and let z > 0 . Then , because of the regularity of xA ( • ) x * , there is a closed

**subset**8 of e such that ( i ) | A ( 81 ) * * — XA ( e ) * * / < E , for every Borel set & ,with ...

Page 2256

Let R = T - 1 . Then , by Theorem VII . 9 . 5 , o ( R ) = { 212 - 1 € ( T ) } U { 0 } .

Since o ( T ) is totally disconnected , each point , in o ( T ) is contained in an

arbitrarily small compact

of o ( T ' ) ...

Let R = T - 1 . Then , by Theorem VII . 9 . 5 , o ( R ) = { 212 - 1 € ( T ) } U { 0 } .

Since o ( T ) is totally disconnected , each point , in o ( T ) is contained in an

arbitrarily small compact

**subset**o of o ( T ) which is open in the relative topologyof o ( T ' ) ...

Page 2309

Our next step is consequently to define such series and develop some of their

basic properties . 4 DEFINITION . ( a ) Let R be an unbounded

complex plane . Let R , be a

defined in RX ...

Our next step is consequently to define such series and develop some of their

basic properties . 4 DEFINITION . ( a ) Let R be an unbounded

**subset**of thecomplex plane . Let R , be a

**subset**of the complex plane , and f a functiondefined in RX ...

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### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

47 other sections not shown

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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