## 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 ( Ar ) = Tx .Further the extension of P by continuity from R ( A ) to R ( A ) is

**unique**. Since P ...Page 1378

نم matrix measure { fus } , i , j = 1 , ... , k of Theorem 23 is

... , k ; Pis = 0 , if i > k or ; > k . Proof . Suppose that 01 , ... , 0x is a determining set

for T. Then it is evident from Theorem 23 that if we define { Pus } , i , = 1 , ... , n ...

نم matrix measure { fus } , i , j = 1 , ... , k of Theorem 23 is

**unique**, and Pij , i , j = 1 ,... , k ; Pis = 0 , if i > k or ; > k . Proof . Suppose that 01 , ... , 0x is a determining set

for T. Then it is evident from Theorem 23 that if we define { Pus } , i , = 1 , ... , n ...

Page 1513

Let Ft be the

and exponents which has the form z - 20 ( 1 + 2 + ... ) near z = 0. Then , since Fa

and Ft together comprise a basis for the solutions of our equation , we have a ...

Let Ft be the

**unique**solution of the equation with these same regular singularitiesand exponents which has the form z - 20 ( 1 + 2 + ... ) near z = 0. Then , since Fa

and Ft together comprise a basis for the solutions of our equation , we have a ...

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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