## Linear operators: Spectral operators |

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Page 2312

... Hahn-

Tz=0 for z in X>{T). Then it follows from Definition 6 that T*y* =0 while y*y ^ 0.

Q.E.D. 8 Lemma. Let X0 be a spectral point of the discrete operator T in a B-

... Hahn-

**Banach**theorem (II. 3. 13) there exists a y* in ?)* such that y*(y) =£ 0, y*Tz=0 for z in X>{T). Then it follows from Definition 6 that T*y* =0 while y*y ^ 0.

Q.E.D. 8 Lemma. Let X0 be a spectral point of the discrete operator T in a B-

**space**X.Page 2313

This is because in Hilbert space we use the Hermitian rather than the pure

the effect of introducing complex conjugates in many of the Hilbert-space

formulas ...

This is because in Hilbert space we use the Hermitian rather than the pure

**Banach space**adjoint, contrary to our practice in other**Banach spaces**. This hasthe effect of introducing complex conjugates in many of the Hilbert-space

formulas ...

Page 2514

Puree Appl. 12, 601-606 (1967). 15. Some properties of spectral maximal spaces

and decomposable operators. Rev. Roumaine Math. Pures Appl. 12, 607-610 (

1967). 16. Some properties of a couple of operators on a

Puree Appl. 12, 601-606 (1967). 15. Some properties of spectral maximal spaces

and decomposable operators. Rev. Roumaine Math. Pures Appl. 12, 607-610 (

1967). 16. Some properties of a couple of operators on a

**Banach space**. Rev.### What people are saying - Write a review

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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