## 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 52

Page 1962

A

according to the relations ( 9 ) * * * 1 = x * H ; X , X EH , and , conversely , any set

x1 , . . . , 7 * of p

related ...

A

**linear functional**ac * on Ho determines p**linear functionals**x1 , . . . , 2 * on Haccording to the relations ( 9 ) * * * 1 = x * H ; X , X EH , and , conversely , any set

x1 , . . . , 7 * of p

**linear functionals**uniquely determines a point x * in ( HP ) *related ...

Page 2066

Now let a * be the continuous

( g ) = x * g for every g in L . Then , since the vector valued function fe is

continuous and bounded as a map from RN into L1 , the vector valued function

fig ( t ) is ...

Now let a * be the continuous

**linear functional**on L , determined by the relation h( g ) = x * g for every g in L . Then , since the vector valued function fe is

continuous and bounded as a map from RN into L1 , the vector valued function

fig ( t ) is ...

Page 2205

Let B be a o - complete Boolean algebra of projections in the B - space X . Then ,

for each wo in X there is a

, Ee B ; ( ii ) if x * Exo = 0 for some E in B , then Exo = 0 . PROOF . By Corollary ...

Let B be a o - complete Boolean algebra of projections in the B - space X . Then ,

for each wo in X there is a

**linear functional**xt in X * with the properties 2 * Exo 20, Ee B ; ( ii ) if x * Exo = 0 for some E in B , then Exo = 0 . PROOF . By Corollary ...

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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