## Linear Operators: Spectral operators |

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Page 2160

It will next be

To see this it will , in view of Corollary II . 3 . 13 , suffice to show that * * ( 20 - y ) =

0 for every linear functional 3 * which vanishes on ( 101 – T ) X . If w * is such a ...

It will next be

**shown**that the vector x - y is in the closure of the manifold ( – T ) X .To see this it will , in view of Corollary II . 3 . 13 , suffice to show that * * ( 20 - y ) =

0 for every linear functional 3 * which vanishes on ( 101 – T ) X . If w * is such a ...

Page 2226

... B is a bounded Boolean algebra of projections on X , then X has an equivalent

norm such that the functionals given by Lemma 3 . 12 can be expressed by

means of a semi - inner product . On the other hand , Walsh [ 2 ; p . 315 ] has

... B is a bounded Boolean algebra of projections on X , then X has an equivalent

norm such that the functionals given by Lemma 3 . 12 can be expressed by

means of a semi - inner product . On the other hand , Walsh [ 2 ; p . 315 ] has

**shown**...Page 2266

It will be

multiplicity on B , Lemma 2 permits us to restrict our attention to 6 . 5 LEMMA .

The set 6 is a dense o - ideal in B . A projection belongs to 6 if and only if it is the

carrier ...

It will be

**shown**that C is a dense o - ideal in B and thus , in defining themultiplicity on B , Lemma 2 permits us to restrict our attention to 6 . 5 LEMMA .

The set 6 is a dense o - ideal in B . A projection belongs to 6 if and only if it is the

carrier ...

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### Contents

SPECTRAL OPERATORS | 1924 |

An Operational Calculus for Bounded Spectral | 1941 |

Part | 1950 |

Copyright | |

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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