## Linear operators: Spectral operators |

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Page 1973

... r) is a

=0, 0£v<vk( k^j, P,(A,) = 1, P<">(A,)=0, 0<v<vt, where the numbers vk are arbitrary

integers with vk'2:mk, k = 1 , . . . , i, will have the property that Pt(r) = E(XS j/1).

... r) is a

**polynomial**P^T) in T and that any**polynomial**Pt with the properties jy>(Aj=0, 0£v<vk( k^j, P,(A,) = 1, P<">(A,)=0, 0<v<vt, where the numbers vk are arbitrary

integers with vk'2:mk, k = 1 , . . . , i, will have the property that Pt(r) = E(XS j/1).

Page 1985

Thus, in particular, <P contains, together with <p, every product P<p where P is a

the assertion that for every pair P, Q of

Thus, in particular, <P contains, together with <p, every product P<p where P is a

**polynomial**in *! 8N . It is clear that convergence <pm -> 99 in <P is equivalent tothe assertion that for every pair P, Q of

**polynomials**in ^ variables we have (3) ...Page 2006

Every operator A in 2l2 uniquely determines two operators S and N in 2I2 with the

following properties: (i) A=S + N, SN = NS; (ii) N* = 0; (iii) for almost all s in S, the

minimal

Every operator A in 2l2 uniquely determines two operators S and N in 2I2 with the

following properties: (i) A=S + N, SN = NS; (ii) N* = 0; (iii) for almost all s in S, the

minimal

**polynomial**of the matrix S(s) of complex numbers has only simple ...### What people are saying - Write a review

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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