## Linear Operators: Spectral operators |

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Page 1960

sum §p of a Hilbert space § with itself p times whose matrix representation (atl)

has, for its

algebra 31 of operators on §. Only a few basic properties of the algebra 21" and

its ...

sum §p of a Hilbert space § with itself p times whose matrix representation (atl)

has, for its

**elements**, the operators a{j which all belong to a commutative S*-algebra 31 of operators on §. Only a few basic properties of the algebra 21" and

its ...

Page 1966

Just as was the case with eB(<5, Z) the

equivalence classes where two matrices A and & are equivalent if A(s) = (s) B for

e-almost all s in S. For a given matrix A = (dlf) in $p we shall use the symbol $sA(

s)e(ds) ...

Just as was the case with eB(<5, Z) the

**elements**of the algebra $." areequivalence classes where two matrices A and & are equivalent if A(s) = (s) B for

e-almost all s in S. For a given matrix A = (dlf) in $p we shall use the symbol $sA(

s)e(ds) ...

Page 2512

34 #8180, 1504 (1967). Allahverdiev, Di. E. 1. On the completeness of a system

of eigen-

normal ones. Doklady Akad. Nauk SSSR 115, 207-210 (1957). (Russian) Math.

34 #8180, 1504 (1967). Allahverdiev, Di. E. 1. On the completeness of a system

of eigen-

**elements**and adjoined**elements**of non- self adjoint operators close tonormal ones. Doklady Akad. Nauk SSSR 115, 207-210 (1957). (Russian) Math.

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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 bounded spectral commuting compact complex numbers complex plane constant contains continuous functions converges Corollary countably additive Definition denote differential operator disjoint Doklady Akad domain eigenvalues elements equation equivalent exists finite number Foias follows from Lemma follows from Theorem formal differential operator formula Hence Hilbert space hypothesis identity inequality inverse Lebesgue Math matrix multiplicity Nauk SSSR norm operators in Hilbert perturbation polynomial preceding 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