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

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Page 1236

We shall prove the second statement first . As each B ; is a continuous linear

functional on D ( T * ) vanishing on D ( T ) , it is

closed extension of T. Since the set of boundary conditions is symmetric , it

follows ...

We shall prove the second statement first . As each B ; is a continuous linear

functional on D ( T * ) vanishing on D ( T ) , it is

**clear**from Lemma 5 ( c ) that T is aclosed extension of T. Since the set of boundary conditions is symmetric , it

follows ...

Page 1652

Then , since Fl « ) 2 Fl , for each F in H ( * ) ( I ) , it is

some F in L ( I ) . Similarly , since Fl « 2100F , for each F in H ( * ) ( I ) and each

index J such that Jl Sk , it is

to ...

Then , since Fl « ) 2 Fl , for each F in H ( * ) ( I ) , it is

**clear**that { F , } converges tosome F in L ( I ) . Similarly , since Fl « 2100F , for each F in H ( * ) ( I ) and each

index J such that Jl Sk , it is

**clear**that if ( Jl Sk , the sequence { a'Fn } convergesto ...

Page 1689

Indeed , if { { m } is a Cauchy sequence in L ( 1 ) , it is

a Cauchy sequence in L ( 1 ) for J Sk , so that there exist functions g , gl in L , ( 1 )

such that limm - com - gl , = 0 and limm - c001m - g'lp = 0. It is then

Indeed , if { { m } is a Cauchy sequence in L ( 1 ) , it is

**clear**from ( i ) that { a'im } isa Cauchy sequence in L ( 1 ) for J Sk , so that there exist functions g , gl in L , ( 1 )

such that limm - com - gl , = 0 and limm - c001m - g'lp = 0. It is then

**clear**from ...### What people are saying - Write a review

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### Contents

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Preliminary Notions | 865 |

Copyright | |

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