## Linear Operators: Spectral theory |

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Page 888

Here we have used the notations A i B and A v B for the intersection and union of two

Here we have used the notations A i B and A v B for the intersection and union of two

**commuting**projections A and B. We recall that these operators are defined by the equations A i B = AB , A v B = A + B - AB and that the intersection ...Page 934

It is trivial to prove that if A and B are

It is trivial to prove that if A and B are

**commuting**self adjoint operators in a Hilbert space , then AB is self adjoint . ... If A is a normal operator and if B is an operator which**commutes**with A , then B**commutes**with A * .Page 935

In analogy with a theorem of N. Jacobson , Kaplansky conjectured that if A

In analogy with a theorem of N. Jacobson , Kaplansky conjectured that if A

**commutes**with AB BA , then the latter is quasi - nilpotent . Putnam [ 3 ] demonstrated that if A and B both**commute**with AB – BA , then AB – BA is a quasi ...### What people are saying - Write a review

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### Contents

BAlgebras | 861 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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additive Akad algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complete Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense derivatives determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure Nauk neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero