## Linear Operators: Spectral theory |

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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 1378

matrix measure { ê ii } , i , j = 1 , . . . , k of Theorem 23 is

= 1 , . . . , k ; Pij = 0 , if i > k or j > k . Proof . Suppose that 07 , . . . , Or is a

determining set for T . Then it is evident from Theorem 23 that if we define { Pis } ,

i , j = 1 ...

matrix measure { ê ii } , i , j = 1 , . . . , k of Theorem 23 is

**unique**, and Pin = Pijs i , j= 1 , . . . , k ; Pij = 0 , if i > k or j > k . Proof . Suppose that 07 , . . . , Or is a

determining set for T . Then it is evident from Theorem 23 that if we define { Pis } ,

i , j = 1 ...

Page 1383

With boundary conditions A and C , the

boundary condition Tz0 = ho is sin vīt . With boundary conditions A , the

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

With boundary conditions A and C , the

**unique**solution of tz0 = lo satisfying theboundary condition Tz0 = ho is sin vīt . With boundary conditions A , the

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

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### Contents

BAlgebras | 861 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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