## 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 89

Page 1926

Since , as this example shows , the theory of normal operators is not an infallible

guide even to the theory of

must revert to more general considerations in attempting to construct the desired

...

Since , as this example shows , the theory of normal operators is not an infallible

guide even to the theory of

**arbitrary**operators in finite dimensional spaces , wemust revert to more general considerations in attempting to construct the desired

...

Page 2101

... T ) satisfies a mth order rate of growth condition , then the nilpotent part N of T

is of type m – 1 ; that is , Nm = 0 . This was proved by Dunford [ 18 ] ; however ,

McCarthy [ 1 , I ] showed that this assertion does not hold in an

.

... T ) satisfies a mth order rate of growth condition , then the nilpotent part N of T

is of type m – 1 ; that is , Nm = 0 . This was proved by Dunford [ 18 ] ; however ,

McCarthy [ 1 , I ] showed that this assertion does not hold in an

**arbitrary**B - space.

Page 2193

Q . E . D . The preceding corollary is not true if the Hilbert space is replaced by an

commuting scalar type spectral operators in a space of continuous functions ...

Q . E . D . The preceding corollary is not true if the Hilbert space is replaced by an

**arbitrary**B - space , for it has been shown by Kakutani [ 15 ] that the sum of twocommuting scalar type spectral operators in a space of continuous functions ...

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### Contents

SPECTRAL OPERATORS XV Spectral Operators | 1924 |

Introduction | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

32 other sections not shown

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analytic apply arbitrary assumed B-space Banach space Boolean algebra Borel sets boundary conditions bounded bounded Borel bounded operator Chapter clear clearly closure commuting compact complex consider constant contained converges Corollary corresponding countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established example exists extension fact finite follows formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator manifold Math Moreover multiplicity norm positive preceding present problem projections PROOF properties prove range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows spectral measure spectral operator spectrum statement strongly subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero