## Linear Operators, Part 2 |

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Page 868

I / 3 is a closed ideal in the commutative B-algebra I then the quotient algebra X/3

is isometrically isomorphic to

maximal. PROOF. If S is not maximal it is properly contained in an ideal and so I/3

...

I / 3 is a closed ideal in the commutative B-algebra I then the quotient algebra X/3

is isometrically isomorphic to

**the field**0/ complex numbers if and only if 8 ismaximal. PROOF. If S is not maximal it is properly contained in an ideal and so I/3

...

Page 891

scalar function f with respect to the operator valued set function E. In the present

chapter we shall only integrate bounded functions f and so the following

discussion of the integral will be restricted to that case. Let Z be

of a set ...

scalar function f with respect to the operator valued set function E. In the present

chapter we shall only integrate bounded functions f and so the following

discussion of the integral will be restricted to that case. Let Z be

**a field**of subsetsof a set ...

Page 1048

If the hypersurface integral of Q over the hypersurface of the unit sphere is zero,

then, whether Q is odd or not, ... Thus the 0'-field Q" of Borel subsets of E: is the

product

...

If the hypersurface integral of Q over the hypersurface of the unit sphere is zero,

then, whether Q is odd or not, ... Thus the 0'-field Q" of Borel subsets of E: is the

product

**a**-**field**of the 0-field QR of Borel subsets of R and the 0'-field .933 of Borel...

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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### Common terms and phrases

Acad adjoint extension adjoint operator algebra Amer analytic B-algebra Banach spaces Borel set boundary conditions boundary values bounded operator closed closure coefficients 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 hypothesis identity inequality integral interval kernel Lemma Let f linear operator linearly independent mapping matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal Paoor partial differential operator Pnoor positive preceding lemma Proc prove real axis real numbers representation satisfies second order Section sequence singular solution spectral set spectral theory square-integrable subspace Suppose symmetric operator topology transform unique unitary vanishes vector zero