## Linear Operators: Spectral operators |

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Page 1983

that the measure spaces (RN, E, ds) and (S, E, ds) are the same. The algebra <t

consists of all d which are continuous on S, that is, all continuous complex ...

**Lebesgue**measure is extended to S by letting the set {oo} have measure zero sothat the measure spaces (RN, E, ds) and (S, E, ds) are the same. The algebra <t

consists of all d which are continuous on S, that is, all continuous complex ...

Page 2409

Before doing so, however, let us note that our argument may be generalized in

two obvious ways. (a) Instead of considering, as above, the space L2(D) of

complex valued

we ...

Before doing so, however, let us note that our argument may be generalized in

two obvious ways. (a) Instead of considering, as above, the space L2(D) of

complex valued

**Lebesgue**measurable functions defined in D and satisfying (7),we ...

Page 2410

Let A(z, z) be a

the space B(X) of all bounded operators in X. Suppose that (35) [A V = sup \A(z, z'

)\ < oo, 2. z'cD and let <p(A) be the integral operator defined by the equation (36)

...

Let A(z, z) be a

**Lebesgue**measurable function defined in D x D, with values inthe space B(X) of all bounded operators in X. Suppose that (35) [A V = sup \A(z, z'

)\ < oo, 2. z'cD and let <p(A) be the integral operator defined by the equation (36)

...

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectra Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

47 other sections not shown

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