## Linear Operators, Part 1 |

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Page 604

Q.E.D. As a final result, we extend the

in T. 10

degree n, and suppose A & P(g(T)). If g($) = [Å–P($)]-1, g is in 37 (T), with no

zeros on ...

Q.E.D. As a final result, we extend the

**spectral**mapping**theorem**to polynomialsin T. 10

**THEOREM**. If P is a polynomial, P(a(T)) = a(P(T)). PRoof. Let P be ofdegree n, and suppose A & P(g(T)). If g($) = [Å–P($)]-1, g is in 37 (T), with no

zeros on ...

Page 609

Independently, Lorch [6] employed the same device and initiated a study of “

are found in Dunford [7], where there is some additional material.

of ...

Independently, Lorch [6] employed the same device and initiated a study of “

**spectral**sets”.**Theorem**3.10 is due to Gelfand [1].**Theorems**3.11, 3.16 and 3.19are found in Dunford [7], where there is some additional material.

**Spectral**theoryof ...

Page 780

On the

186 (1939). 2. Bounded self-adjoint operators and the problem of moments. Bull.

Amer. Math. Soc. 45, 303-306 (1939). Lengyel, B. A., and Stone, M. H. 1.

On the

**spectral theorem**of self-adjoint operators. Acta Sci. Math. Szeged 9, 174–186 (1939). 2. Bounded self-adjoint operators and the problem of moments. Bull.

Amer. Math. Soc. 45, 303-306 (1939). Lengyel, B. A., and Stone, M. H. 1.

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### Contents

A Settheoretic Preliminaries | 1 |

Convergence and Uniform Convergence of Generalized | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

27 other sections not shown

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