## Linear operators: Spectral operators |

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Page 1925

The problem of extending this reduction theory to non-

the most important unsolved problems in the theory of linear operations.

Consider, for instance, the problem of finding a resolution of the identity for the

formal ...

The problem of extending this reduction theory to non-

**normal operators**is one ofthe most important unsolved problems in the theory of linear operations.

Consider, for instance, the problem of finding a resolution of the identity for the

formal ...

Page 2005

where h is Hilbert's singular integral (34), is an

adjoint, and not

and 6, a spectral

where h is Hilbert's singular integral (34), is an

**operator**in 9l2 which is not selfadjoint, and not

**normal**unless i( a — b) is self adjoint but is, for many choices of aand 6, a spectral

**operator**. To see this, equation (35) shows that the condition ...Page 2560

On the convergence of series of eigenfunctions of a completely continuous

operator in Banach spaces. Sibirsk. Mat. 2. 4 706-708 (1963). (Russian) Math.

Rev. 28 #475, 99 (1964). Putnam, C. R. 19. On square roots of

Proc.

On the convergence of series of eigenfunctions of a completely continuous

operator in Banach spaces. Sibirsk. Mat. 2. 4 706-708 (1963). (Russian) Math.

Rev. 28 #475, 99 (1964). Putnam, C. R. 19. On square roots of

**normal operators**.Proc.

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

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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