## Linear Operators: Spectral theory |

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Page 889

As will be seen in the next section, a normal operator T in Hilbert space $5

determines a spectral measure which is defined on the Boolean algebra 3 of all

measure ...

As will be seen in the next section, a normal operator T in Hilbert space $5

determines a spectral measure which is defined on the Boolean algebra 3 of all

**Borel**sets in the plane and which satisfies (iv) for every 6 e 3. This spectralmeasure ...

Page 913

We can clearly suppose that yo) = 1. Let yo, y1, y2, ... be an orthonormal basis for

$5, whose initial element is yo. Let E be the spectral resolution for T and let v, (e)

= (E(e)ya, ya) for each

We can clearly suppose that yo) = 1. Let yo, y1, y2, ... be an orthonormal basis for

$5, whose initial element is yo. Let E be the spectral resolution for T and let v, (e)

= (E(e)ya, ya) for each

**Borel**sete. Using the Lebesgue decomposition theorem ...Page 1900

(See also Boolean ring) definition, (43) properties, (44) representation of, (44)

Boolean ring, definition, (40) representation of, I.1.2.1 (41)

definition, III.5.10 (137)

891) ...

(See also Boolean ring) definition, (43) properties, (44) representation of, (44)

Boolean ring, definition, (40) representation of, I.1.2.1 (41)

**Borel**field of sets,definition, III.5.10 (137)

**Borel**function, X.1 (891)**Borel**measurable function, X.I (891) ...

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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