## 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

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 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 the set ...

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 the set ...

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### Contents

SPECTRAL OPERATORS 1937 1941 1945 XV Spectral Operators | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

29 other sections not shown

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