## Linear operators: Spectral operators |

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Page 1945

Bounded Spectral Operators in Hubert Space What is the relationship between

the bounded spectral operators in a

operators in §? The central result in this direction is a theorem of Wermer which ...

Bounded Spectral Operators in Hubert Space What is the relationship between

the bounded spectral operators in a

**Hilbert space**£> and the bounded normaloperators in §? The central result in this direction is a theorem of Wermer which ...

Page 2169

Self Adjoint Operators in

how the theory of spectral operators may be applied to yield the classical spectral

theorem in

adjoint ...

Self Adjoint Operators in

**Hilbert Space**It is the purpose of this section to showhow the theory of spectral operators may be applied to yield the classical spectral

theorem in

**Hilbert space**, that is, the theorem asserting that a bounded selfadjoint ...

Page 2528

Finite dimensional perturbations in Banach spaces. Amer. J. Math ... Weak limits

of powers of a contraction in

spectrale et la théorie spectrale des opérateurs généraux d'un espace de Hilbert.

Bull.

Finite dimensional perturbations in Banach spaces. Amer. J. Math ... Weak limits

of powers of a contraction in

**Hilbert space**. Proc. ... La mesure harmonique-spectrale et la théorie spectrale des opérateurs généraux d'un espace de Hilbert.

Bull.

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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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### Common terms and phrases

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