## Linear Operators: Spectral theory |

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Page 935

then AB –

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 ...

then AB –

**BA is**a two-sided topological divisor of zero. In analogy with a theoremof 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 ...

Page 1246

A continuity argument shows that (Bar, y) = (a, y) for a e S), ye Q(T), and that |

itself, we see B is an operator in § of norm at most one. Since for a and y in the ...

A continuity argument shows that (Bar, y) = (a, y) for a e S), ye Q(T), and that |

**Ba**'**s**|Barlı is a for a e $). Thus regarding B as a mapping of § into a dense subset ofitself, we see B is an operator in § of norm at most one. Since for a and y in the ...

Page 1264

Then f(A,) → f(A) strongly for each bounded function f of a real variable which is

continuous except on a closed set C such ... Principle, Heisenberg) Let A and B

be self adjoint operators in Hilbert space such that 3), H Q(AB) n Q(

Then f(A,) → f(A) strongly for each bounded function f of a real variable which is

continuous except on a closed set C such ... Principle, Heisenberg) Let A and B

be self adjoint operators in Hilbert space such that 3), H Q(AB) n Q(

**BA**)**is**dense.### What people are saying - Write a review

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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additive Akad algebra Amer analytic applied 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 determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function function f given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math measure multiplicity 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