## Linear Operators: Spectral Theory : Self Adjoint Operators in Hilbert Space, Volume 2 |

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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

...

Page 2448

In the

results , due to Robert E . L . Turner , concerning the spectral character of certain

classes of compact operators . We begin by generalizing Theorem 2 . 1 .

In the

**present**section we shall illustrate this assertion by proving a number ofresults , due to Robert E . L . Turner , concerning the spectral character of certain

classes of compact operators . We begin by generalizing Theorem 2 . 1 .

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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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### Common terms and phrases

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 formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator manifold Math Moreover multiplicity norm normal 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