## Linear Operators: Spectral theory |

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Page 1459

corollary follows from Corollary 7 and Definition 25(b). Q.E.D. 31 CoRollARY.

Suppose in addition to the hypotheses of Theorem 8 that the coefficients p, are

real ...

**PROOF**. It is obvious from Definition 20 that t is bounded below. Thus the presentcorollary follows from Corollary 7 and Definition 25(b). Q.E.D. 31 CoRollARY.

Suppose in addition to the hypotheses of Theorem 8 that the coefficients p, are

real ...

Page 1724

By Green's formula, proved in the last paragraph of Section 2, this equation is

valid if f and g are in Co(I). It follows as in the

that there exist bounded operators A and B mapping H'."(I) into itself, such that (Tf

, ...

By Green's formula, proved in the last paragraph of Section 2, this equation is

valid if f and g are in Co(I). It follows as in the

**proof**of formula (6) of Corollary 11that there exist bounded operators A and B mapping H'."(I) into itself, such that (Tf

, ...

Page 1750

We shall see, however, that this fact is needed in the course of the

Theorem 1, and shall prove it by a direct method where it is needed. Remark 2.

The theorem is false if no boundedness restriction is imposed on the coefficient

matrices ...

We shall see, however, that this fact is needed in the course of the

**proof**ofTheorem 1, and shall prove it by a direct method where it is needed. Remark 2.

The theorem is false if no boundedness restriction is imposed on the coefficient

matrices ...

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Spectral Representation | 909 |

Copyright | |

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