## Linear Operators: Spectral operators |

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Page 1989

The basic

is defined in terms of the Fourier transform F on H by the equation ( 16 ) ( 15 ) elo

) = F - u ( o ) F , 0e , where ulo ) is the multiplication projection defined as ( u ( o )

...

The basic

**spectral measure**e on which is used to define the algebras A and APis defined in terms of the Fourier transform F on H by the equation ( 16 ) ( 15 ) elo

) = F - u ( o ) F , 0e , where ulo ) is the multiplication projection defined as ( u ( o )

...

Page 2107

been studied in connection with ( partially ) ordered spaces by Schaefer [ 7 , 10 ,

11 ] , Schaefer and Walsh [ 1 ] , and Walsh [ 1 , 2 , 3 ] . We shall give a condensed

...

**Spectral measures**, locally convex spaces and order .**Spectral measures**havebeen studied in connection with ( partially ) ordered spaces by Schaefer [ 7 , 10 ,

11 ] , Schaefer and Walsh [ 1 ] , and Walsh [ 1 , 2 , 3 ] . We shall give a condensed

...

Page 2110

One of the most surprising results due to Walsh [ 2 ] is the result that if u is an

equicontinuous Borel

a space E in which closed bounded sets are compact ( for example , a Montel ...

One of the most surprising results due to Walsh [ 2 ] is the result that if u is an

equicontinuous Borel

**spectral measure**into the space of continuous operators ina space E in which closed bounded sets are compact ( for example , a Montel ...

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### Contents

SPECTRAL OPERATORS | 1924 |

An Operational Calculus for Bounded Spectral | 1941 |

Part | 1950 |

Copyright | |

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### Common terms and phrases

adjoint operator analytic apply arbitrary assume B-space Banach space Boolean algebra Borel sets boundary conditions bounded bounded operator Chapter clear closed commuting compact complex consider constant contained continuous converges Corollary corresponding countably additive defined Definition denote dense determined differential operator discrete 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 Math Moreover multiplicity norm positive preceding present problem projections PROOF properties proved range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows similar spectral measure spectral operator spectrum subset subspace sufficiently Suppose Theorem theory topology unbounded uniform uniformly unique valued vector weakly zero