## Linear Operators: Spectral operators |

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Page 1990

This elementary observation suggests that it might be easier to give certain

convolutions an integral representation if we use the integral of

functions , and this we shall do . We begin by defining the convolution integral (

19 ) ...

This elementary observation suggests that it might be easier to give certain

convolutions an integral representation if we use the integral of

**vector**valuedfunctions , and this we shall do . We begin by defining the convolution integral (

19 ) ...

Page 2160

It will next be shown that the

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

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

It will next be shown that the

**vector**x - y is in the closure of the manifold ( 101 – T) X . To see this it will , in view of Corollary II . 3 . 13 , suffice to show that x * ( x - y

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

Page 2266

The cyclic subspace M ( x ) spanned by a

Ee B will be said to satisfy the countable chain condition if every family of disjoint

projections in B bounded by E is at most countable . We shall denote by 6 the ...

The cyclic subspace M ( x ) spanned by a

**vector**x is sp { Ex | E € B } . A projectionEe B will be said to satisfy the countable chain condition if every family of disjoint

projections in B bounded by E is at most countable . We shall denote by 6 the ...

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

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adjoint operator analytic applications arbitrary assumed B-space Banach space belongs Boolean algebra Borel sets boundary bounded bounded operator Chapter clear closed commuting compact complex condition consider constant contained continuous converges Corollary corresponding countably additive defined Definition denote dense determined 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 perturbation plane 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 uniformly unique valued vector weakly zero