## 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 28

Page 1974

It is clear that ( iii )

that ( i )

suppose that for some i = 1 , . 1974 XV . 10 . 4 xv . SPECTRAL OPERATORS.

It is clear that ( iii )

**implies**( i ) , and so to prove the lemma it will suffice to provethat ( i )

**implies**( ii ) . Let ( a ) sup e - ess sup \ E ( o ; ( s ) ) = K < 00 , DESSES andsuppose that for some i = 1 , . 1974 XV . 10 . 4 xv . SPECTRAL OPERATORS.

Page 2174

In a Hilbert space the condition that lettr | SM for all te R

equivalent to a self adjoint operator and hence is a scalar type operator with real

spectrum . ( This follows from Lemma XV . 6 . 1 which

group G ...

In a Hilbert space the condition that lettr | SM for all te R

**implies**that T isequivalent to a self adjoint operator and hence is a scalar type operator with real

spectrum . ( This follows from Lemma XV . 6 . 1 which

**implies**that the boundedgroup G ...

Page 2218

Q . E . D . The section will be concluded with two theorems of Bade which belong

to that interesting collection of results in B - spaces concerning conditions when

weak convergence

...

Q . E . D . The section will be concluded with two theorems of Bade which belong

to that interesting collection of results in B - spaces concerning conditions when

weak convergence

**implies**strong convergence . 27 THEOREM . If a generalized...

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### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

28 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 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