## Linear Operators: Spectral theory |

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Page 935

then A B –

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 ...

then A B –

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

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 that ... Principle, Heisenberg) Let A and

B be self adjoint operators in Hilbert space such that oo - Q(AB) n \(

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 that ... Principle, Heisenberg) Let A and

B be self adjoint operators in Hilbert space such that oo - Q(AB) n \(

**BA**)**is**dense.Page 1533

For the sake of simplicity we shall also assume that 2k

dependent and independent variables outlined above we have

For the sake of simplicity we shall also assume that 2k

**is**not an integer, so that (**B-A**)f = 0 has solutions**S**, of the form to/**(1+...) at t = 0. By the transformations ofdependent and independent variables outlined above we have

**S**.(t, 2) = toe-toq ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Spectral Representation | 909 |

Copyright | |

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adjoint extension adjoint operator algebra Amer analytic B-algebra Banach Borel set boundary conditions boundary values bounded operator closed closure Cº(I coefficients complete complex numbers continuous function converges Corollary deficiency indices Definition denote dense differential equations Doklady Akad domain eigenfunctions eigenvalues element essential spectrum exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function f Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval kernel Lemma Let f linear operator linearly independent mapping Math matrix measure Nauk SSSR N.S. neighborhood norm open set operators in Hilbert orthogonal orthonormal Plancherel's theorem positive Proc PRoof prove real numbers satisfies sequence singular ſº solution spectral spectral set spectral theory square-integrable subspace Suppose theory To(r topology transform unique unitary vanishes vector zero