## Linear Operators: Self Adjoint Operators in Hilbert Space. Spectral theory. Part II |

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Page 1247

Q.E.D. The next lemma shows that a positive self adjoint transformation has a

a

2 ...

Q.E.D. The next lemma shows that a positive self adjoint transformation has a

**unique**positive “ square root ” . 3 LEMMA . ... self adjoint transformation , there isa

**unique**positive self adjoint transformation A such that A2 = T. Proof . By Lemma2 ...

Page 1250

Since A is

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

Since P is zero on R ( A ) ' it follows that P is

8.

Since A 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 is zero on R ( A ) ' it follows that P is

**uniquely**determined by T. Q.E.D. 0 .8.

Page 1513

Let F. be the

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

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

Let F. be the

**unique**solution of the equation with these same regular singularitiesand exponents which has the form 2-2 ( 1 + + ... ) 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

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Preliminary Notions | 865 |

Copyright | |

61 other sections not shown

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