## Linear Operators: Spectral theory |

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Page 1420

If A is considered as a subset of H , then the restriction of T ( t ' ) to A is a

continuous mapping of A into H . Then , assuming that ttt ' has a non -

leading coefficient , ( A ) the Hilbert spaces D ( Ti ( t + t ' ) ) and D ( T1 ( T ) ) have

the same ...

If A is considered as a subset of H , then the restriction of T ( t ' ) to A is a

continuous mapping of A into H . Then , assuming that ttt ' has a non -

**zero**leading coefficient , ( A ) the Hilbert spaces D ( Ti ( t + t ' ) ) and D ( T1 ( T ) ) have

the same ...

Page 1432

Suppose first that the end point under consideration is finite so that without loss of

generality we can suppose it to be at

by the leading coefficient an of T , we can write the equation ( T - 2 ) } = 0 in the ...

Suppose first that the end point under consideration is finite so that without loss of

generality we can suppose it to be at

**zero**. Then , dividing through if necessaryby the leading coefficient an of T , we can write the equation ( T - 2 ) } = 0 in the ...

Page 1727

By ( 1 ) and by the definitions ( 2 ) , ( 3 ) , and ( 5 ) of Su , it follows that ( 7 ) ( S29 )

( x ) = 0 , 9€ C ( En ) , - k Smin ( L ) S max ( L ) Sk , if one of x7 , . . . , xn is

Suppose that we let 1 , denote the cube 1 . = { x € E " | | X : 51 , i = 1 , . . . , n } .

By ( 1 ) and by the definitions ( 2 ) , ( 3 ) , and ( 5 ) of Su , it follows that ( 7 ) ( S29 )

( x ) = 0 , 9€ C ( En ) , - k Smin ( L ) S max ( L ) Sk , if one of x7 , . . . , xn is

**zero**.Suppose that we let 1 , denote the cube 1 . = { x € E " | | X : 51 , i = 1 , . . . , n } .

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### Contents

IX | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Compact Groups | 945 |

Copyright | |

46 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

additive adjoint operator algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently consider constant contains continuous converges Corollary corresponding defined Definition denote dense derivatives determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero