## Linear operators: Spectral operators |

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Page 2227

Introduction It was shown in the course of Chapters XII, XIII, and XIV that in order

to apply the

differential operators it is first necessary to extend the

...

Introduction It was shown in the course of Chapters XII, XIII, and XIV that in order

to apply the

**spectral theory**of Hermitian operators to ordinary and partialdifferential operators it is first necessary to extend the

**spectral theory**of bounded...

Page 2559

Spectral operators Nelson Dunford, Jacob T. Schwartz. 4. Ein verallgemeinertes

Spektralproblem fur kompakte Uneare ... Pincus, J. D. (see also Koppelman, W.)

1. On the

Spectral operators Nelson Dunford, Jacob T. Schwartz. 4. Ein verallgemeinertes

Spektralproblem fur kompakte Uneare ... Pincus, J. D. (see also Koppelman, W.)

1. On the

**spectral theory**of singular integral operators. Trans. Amer. Math. Soc.Page 2571

The minimum modulus of a linear operator, and its use for estimates in

ascent, descent, nullity and defect of linear operators. Math. Ann. 163, 18-49 ...

The minimum modulus of a linear operator, and its use for estimates in

**spectral****theory**. Studia Math. (Ser. Specjalna) Zeszyt 1, 131-132 (1963). 18. Theorems onascent, descent, nullity and defect of linear operators. Math. Ann. 163, 18-49 ...

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

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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