## Linear Operators, Part 2 |

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Page 1250

Finally we show that the decomposition T = PA of the theorem is

A is

Further the extension of P by continuity from R ( A ) to R ( A ) is

Finally we show that the decomposition T = PA of the theorem is

**unique**. ... SinceA is

**unique**, P is**uniquely**determined on R ( A ) by the equation of P ( Ax ) = Tx .Further the extension of P by continuity from R ( A ) to R ( A ) is

**unique**. Since P ...Page 1283

Thus , equation ( e ' ) has the

H = ( - 1 ) P H . j = 0 Since all the terms in equation ( e ) but the first are absolutely

continuous , it follows that F is absolutely continuous . Thus Theorem 1 is ...

Thus , equation ( e ' ) has the

**unique**solution ( cf . Lemma VII . 3 . 4 ) F = ( 1 + 0 ) -H = ( - 1 ) P H . j = 0 Since all the terms in equation ( e ) but the first are absolutely

continuous , it follows that F is absolutely continuous . Thus Theorem 1 is ...

Page 1383

With boundary conditions A and C , the

boundary condition 130 = ho is sin vīt . With boundary conditions A , the

eigenvalues are consequently to be determined from the equation sin vă = 0 .

With boundary conditions A and C , the

**unique**solution of 730 = ho satisfying theboundary condition 130 = ho is sin vīt . With boundary conditions A , the

eigenvalues are consequently to be determined from the equation sin vă = 0 .

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

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