## Linear operators: Spectral operators |

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Page 2264

theory for Boolean algebras of projections in a B-space X will be developed and

applied to show that, under certain restrictions, a scalar type operator S in X is ...

**Multiplicity**Theory and Spectral Representation The methods and ... A**multiplicity**theory for Boolean algebras of projections in a B-space X will be developed and

applied to show that, under certain restrictions, a scalar type operator S in X is ...

Page 2283

Let B be a complete Boolean algebra of projections in a Banach space X and let

B* be the Boolean algebra of adjoints in B*. Then a projection E in B has finite

uniform

n.

Let B be a complete Boolean algebra of projections in a Banach space X and let

B* be the Boolean algebra of adjoints in B*. Then a projection E in B has finite

uniform

**multiplicity**n if and only if its adjoint E* in B* has finite uniform**multiplicity**n.

Page 2288

The

Dieudonne" [20] had previously obtained a

the adjoint X* of the underlying Banach space X is separable (which implies the ...

The

**multiplicity**theory as presented in Section 3 is due to W. G. Bade [5]. J.Dieudonne" [20] had previously obtained a

**multiplicity**theory in the case wherethe adjoint X* of the underlying Banach space X is separable (which implies the ...

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

47 other sections not shown

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adjoint operator algebra of projections Amer analytic arbitrary asymptotic B-space Banach space Boolean algebra Borel sets boundary conditions bounded Borel function bounded linear operator bounded operator commuting compact complex numbers complex plane constant contains continuous functions converges Corollary countably additive Definition denote dense differential operator disjoint Doklady Akad domain eigenvalues elements equation exists finite number Foias follows from Lemma follows from Theorem formal differential operator formula Hence Hilbert space hypothesis identity inequality inverse Lebesgue Math matrix measurable functions multiplicity Nauk SSSR norm normal operators operators in Hilbert perturbation polynomial Proof properties prove quasi-nilpotent restriction Russian satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum strong operator topology subset Suppose trace class type spectral operator unbounded uniformly bounded unique vector weakly complete zero