## Linear Operators: Spectral operators |

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Page 2249

... and it follows immediately from

This proves the first two assertions of the present

olf ( T ) ) = f ( o ( T ) ) , which is part of the final assertion of the present

... and it follows immediately from

**Theorem**9 ( v ) that ( 1 / f ) ( A ) is bounded .This proves the first two assertions of the present

**theorem**, and also the inclusionolf ( T ) ) = f ( o ( T ) ) , which is part of the final assertion of the present

**theorem**.Page 2403

concrete situation to be studied , to hypotheses ( a ) and ( c ) of

overall plan will be as follows . First we shall prove an inequality for integral

operators ( Lemma 5 below ) which is elementary in the sense that it relates only

to ...

concrete situation to be studied , to hypotheses ( a ) and ( c ) of

**Theorem**1 . Ouroverall plan will be as follows . First we shall prove an inequality for integral

operators ( Lemma 5 below ) which is elementary in the sense that it relates only

to ...

Page 2418

exists almost everywhere for each fe ip ( D , Y ) , and , using Lemma 5 once more

, the integral ( 74 ) $ _ 14462 " , 2 ) { S , 1 4363 , | 15 ( 2 ) de ' dy de dy exists for

almost all z " e D . Therefore , by Tonelli ' s

exists almost everywhere for each fe ip ( D , Y ) , and , using Lemma 5 once more

, the integral ( 74 ) $ _ 14462 " , 2 ) { S , 1 4363 , | 15 ( 2 ) de ' dy de dy exists for

almost all z " e D . Therefore , by Tonelli ' s

**theorem**( III . 11 . 14 ) , the integral ...### What people are saying - Write a review

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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