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

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Results 1-3 of 86

Page 1931

Of course it is not

identity defined on the Borel sets of the plane is uniquely determined by the

spectral operator T . This is the case , but until it is proved we refer to any such

spectral ...

Of course it is not

**clear**to begin with that a countably additive resolution of theidentity defined on the Borel sets of the plane is uniquely determined by the

spectral operator T . This is the case , but until it is proved we refer to any such

spectral ...

Page 2053

In the examples of Theorems 19 and 21 we did not appeal to the general theory ,

as it was

an arbitrary y in Hp . It is even

In the examples of Theorems 19 and 21 we did not appeal to the general theory ,

as it was

**clear**from the form of exp tÂ that T ( t ) o was differentiable for t > 0 andan arbitrary y in Hp . It is even

**clear**that the nth order derivative T ( n ) ( t ) exists ...Page 2159

It is

second expression for Yn that it is closed , and it follows from ( G ) that every point

in y is in one of the sets Yn . Thus , by the Baire category theorem ( cf . 1 . 6 .

It is

**clear**that the union of intervals of constancy is open . ... It is**clear**from thesecond expression for Yn that it is closed , and it follows from ( G ) that every point

in y is in one of the sets Yn . Thus , by the Baire category theorem ( cf . 1 . 6 .

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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