## 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 x * which vanishes on ( 101 – T ) X . If xc * is ...

It will next be shown that the

**vector**x - y is in the closure of the manifold ( 1 . 1 – 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 ( 101 – T ) X . If xc * is ...

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 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 6 the set

...

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