## 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**valued,functions, and this we shall do. We begin by defining the convolution integral (19)

...

Page 2160

It will next be shown that the

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 x* which vanishes on (X0I — T)X. If x* is such a ...

It will next be shown that the

**vector**x — y is in the closure of the manifold (X0I —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 x* which vanishes on (X0I — T)X. If x* is such a ...

Page 2266

The cyclic subspace 9[R(x) spanned by a

e 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 9[R(x) spanned by a

**vector**x is sp{Ex\ E e E). A projection 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

...

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

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