## Linear Operators, Part 2 |

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Page 884

The study of ideal theory in B - algebra was inaugurated by Gelfand [ 1 ] to whom

most of the

Lemma 3.5 by using a fairly deep

The study of ideal theory in B - algebra was inaugurated by Gelfand [ 1 ] to whom

most of the

**results**given in Section 1 are due . ... In their proof , they provedLemma 3.5 by using a fairly deep

**result**of Šilov that was not generally available .Page 1419

We will show that ( m ) 2 \ | ( mi + 1 ) 2 / ( mi + 2 ) 2 ... , which will clearly establish

the desired

t ) and fı ( t ) = + | ( 28 + 1 - t ) . We have ( -1 ) " = 9 ( -1 ) , t = qut , where qı ( t ) = 9 ...

We will show that ( m ) 2 \ | ( mi + 1 ) 2 / ( mi + 2 ) 2 ... , which will clearly establish

the desired

**result**. On the interval [ si + 1 , mi + 1 ] , consider the two functions -f (t ) and fı ( t ) = + | ( 28 + 1 - t ) . We have ( -1 ) " = 9 ( -1 ) , t = qut , where qı ( t ) = 9 ...

Page 1433

In case the indicial equation has two roots which differ by an integer or has

multiple roots , a corresponding

solutions of [ * ] may have a more complex form , involving logarithmic terms . We

shall not ...

In case the indicial equation has two roots which differ by an integer or has

multiple roots , a corresponding

**result**may be stated ; but here the basis forsolutions of [ * ] may have a more complex form , involving logarithmic terms . We

shall not ...

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

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 complex 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 matrix measure multiplicity neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result Russian satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero