## Linear Operators, Part 2 |

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Page 865

An

with 0 ;& eo qé e clearly has 00(1) Q a(a:). The following lemma shows that the

opposite inclusion holds in case In has the same unit as Iii. 9 LEMMA. Let .1: be ...

An

**element**.2 in a B-subalgebra of the form In = eoieo where eo is an idempotentwith 0 ;& eo qé e clearly has 00(1) Q a(a:). The following lemma shows that the

opposite inclusion holds in case In has the same unit as Iii. 9 LEMMA. Let .1: be ...

Page 877

Then an

Consequently the spectrum of y as an

as an

the ...

Then an

**element**y in 'Q has an inverse in I if and only if it has an inverse inConsequently the spectrum of y as an

**element**of 'Q is the same as its spectrumas an

**element**0/ I. Paoor. If y-1 exists as an**element**of Q then, since I and havethe ...

Page 1339

0)/.-<1>7,W Md/1) < co will be denoted by Lg({_u,-,}). An

will be said to be a. {,u,,}-null function if [F] = 0. The set of all equivalence classes

of

0)/.-<1>7,W Md/1) < co will be denoted by Lg({_u,-,}). An

**element**F of L2({,u,-,})will be said to be a. {,u,,}-null function if [F] = 0. The set of all equivalence classes

of

**elements**of Lg({Jui,}) modulo {/4”}-null functions will be denoted by L2({'u,-,}).### 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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### 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