## 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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Page 2098

T. = SWE. (. 42. ) +. N. ,. when N is a quasi - nilpotent which may not commute

with T . The conditions imply that o ( T ) = 0 , ( T ) . See also Deal [ 2 ] . The

following

Smart [ 2 ] .

T. = SWE. (. 42. ) +. N. ,. when N is a quasi - nilpotent which may not commute

with T . The conditions imply that o ( T ) = 0 , ( T ) . See also Deal [ 2 ] . The

following

**result**was proved by Sine [ 1 ] , using techniques similar to those inSmart [ 2 ] .

Page 2108

This

scalar type operators . We shall say that an element a e A is scalar ( although

Schaefer [ 10 ; p . 143 ] used the word “ spectral ” ) if there exists a compact space

...

This

**result**throws light on when the sum and product of scalar type operators arescalar type operators . We shall say that an element a e A is scalar ( although

Schaefer [ 10 ; p . 143 ] used the word “ spectral ” ) if there exists a compact space

...

Page 2214

Q . E . D . The preceding material of the present section was largely preliminary to

the following basic

THEOREM . Let B be a bounded Boolean algebra of projections in a weakly ...

Q . E . D . The preceding material of the present section was largely preliminary to

the following basic

**result**of Bade , which was described in the introduction . 18THEOREM . Let B be a bounded Boolean algebra of projections in a weakly ...

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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