## 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 1909

We

Remarks , especially in Section XX.6 , give the physical interpretations as well as

a brief discussion of past and

We

**present**the abstract operator theory in the text , and then in the Notes andRemarks , especially in Section XX.6 , give the physical interpretations as well as

a brief discussion of past and

**present**related problems . The first heretofore ...Page 2058

In explaining these implications in nonmathematical terms he envisaged , in his

Philosophical Essay on Probabilities ( 1814 ) , a kind of superhuman calculator

who could , upon having complete knowledge of the

...

In explaining these implications in nonmathematical terms he envisaged , in his

Philosophical Essay on Probabilities ( 1814 ) , a kind of superhuman calculator

who could , upon having complete knowledge of the

**present**state of the universe...

Page 2227

The

spectral operators . We begin by defining a closed spectral operator and its

resolution of the identity , and showing that the latter is unique . Then a functional

...

The

**present**chapter is an attempt to make the corresponding step in the theory ofspectral operators . We begin by defining a closed spectral operator and its

resolution of the identity , and showing that the latter is unique . Then a functional

...

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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