## Linear Operators: Spectral theory |

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Page 888

where a, 6 are arbitrary

used the notations A a B and A v B for the intersection and union of two

commuting projections A and B. We recall that these operators are defined by the

...

where a, 6 are arbitrary

**spectral**sets and where 4 is the void set. Here we haveused the notations A a B and A v B for the intersection and union of two

commuting projections A and B. We recall that these operators are defined by the

...

Page 933

79], where the relation of the

other questions are investigated. Halmos [9] also considers the relation of the

...

79], where the relation of the

**spectra**of A and its minimal normal extension andother questions are investigated. Halmos [9] also considers the relation of the

**spectra**. The**spectral**sets of von Neumann. If T is a bounded linear operator in a...

Page 1920

G.(1614)

(892)

VII.3.5 (567) of an element in a B-algebra, IX.1.2 (861) properties, VII.3.4 (567), ...

G.(1614)

**Spectral**measure, X.1 (888) countably additive, X.I (889) self adjoint, X.I(892)

**Spectral**multiplicity theory, definition, X.5 (913)**Spectral**radius, definition,VII.3.5 (567) of an element in a B-algebra, IX.1.2 (861) properties, VII.3.4 (567), ...

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

34 other sections not shown

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additive Akad algebra Amer analytic applied assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complete Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function function f given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math measure multiplicity neighborhood norm obtained partial positive preceding present problem projection PRoof properties prove range regular remark representation respectively restriction result satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero