## Linear Operators: Spectral theory |

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Page 922

2 , ... , are defined . 1 LEMMA . Let S , T , S. , T. , n 2 1 be bounded linear

operators in Hilbert space with Sn → S , T , → T in the strong operator

Then S ...

**topology**, i.e. , T , & → Tx for every x in the space upon which the operators T , T ,2 , ... , are defined . 1 LEMMA . Let S , T , S. , T. , n 2 1 be bounded linear

operators in Hilbert space with Sn → S , T , → T in the strong operator

**topology**.Then S ...

Page 1420

( a ' ) The

be a sequence in D ( Ti ( t ) ) . Suppose that { / } converges to zero in the

of D ...

( a ' ) The

**topology**of the Hilbert space D ( T1 ( T ) ) is the same as its relative**topology**as a subspace of the Hilbert space D ( T2 ( t + 7 ' ) ) . Indeed , let { { n }be a sequence in D ( Ti ( t ) ) . Suppose that { / } converges to zero in the

**topology**of D ...

Page 1921

F ( 1550 ) Subadditive function , definition , ( 618 ) Subbase for a

( 10 ) criterion for , 1.4.8 ( 11 ) Subspace , of a linear space , ( 36 ) . ( See also

Manifold ) Summability , of Fourier series , IV.14.34–51 ( 361-364 ) general ...

F ( 1550 ) Subadditive function , definition , ( 618 ) Subbase for a

**topology**, 1.4.6( 10 ) criterion for , 1.4.8 ( 11 ) Subspace , of a linear space , ( 36 ) . ( See also

Manifold ) Summability , of Fourier series , IV.14.34–51 ( 361-364 ) general ...

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