## Linear Operators: Spectral theory |

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Page 1010

resentations as an Ly - space and in this setting the class of

space H . A bounded linear operator T is said to be a

case ...

resentations as an Ly - space and in this setting the class of

**HilbertSchmidt****operators**may be defined as follows . ... complete orthonormal set in the Hilbertspace H . A bounded linear operator T is said to be a

**Hilbert**-**Schmidt operator**incase ...

Page 1013

The operator T is compact ( cf . Exercise X . 8 . 5 ) , but it is not in HS . It has been

noted in the preceding discussion that the class of

forms a Banach algebra ( without identity ) under the norm | | . | | . It may readily

be ...

The operator T is compact ( cf . Exercise X . 8 . 5 ) , but it is not in HS . It has been

noted in the preceding discussion that the class of

**Hilbert**-**Schmidt operators**forms a Banach algebra ( without identity ) under the norm | | . | | . It may readily

be ...

Page 1132

Nelson Dunford, Jacob T. Schwartz. If K is a

there exists a unique set Kij ( s , t ) of kernels representing K in the sense that ( 3 )

K [ / ( s ) , [ 2 ( s ) , . . . ] = [ 81 ( s ) , 82 ( s ) , . . . ] where ( 4 ) 8 : ( 8 ) = į Kj ( s , t ) } ...

Nelson Dunford, Jacob T. Schwartz. If K is a

**Hilbert**-**Schmidt operator**in L2 ( A ) ,there exists a unique set Kij ( s , t ) of kernels representing K in the sense that ( 3 )

K [ / ( s ) , [ 2 ( s ) , . . . ] = [ 81 ( s ) , 82 ( s ) , . . . ] where ( 4 ) 8 : ( 8 ) = į Kj ( s , t ) } ...

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### Contents

IX | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Compact Groups | 945 |

Copyright | |

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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