## Linear Operators: Spectral theory |

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Page 1856

The singular elements of a

1947 ) . 5 . Isomorphic groups of linear transformations . Amer . J . Math . 72 , 451

- 464 ( 1950 ) .

The singular elements of a

**Banach**algebra . Duke Math . J . 14 , 1063 - 1077 (1947 ) . 5 . Isomorphic groups of linear transformations . Amer . J . Math . 72 , 451

- 464 ( 1950 ) .

**Banach**algebras with an adjoint operation . Ann . of Math .Page 1864

Weak compactness in

Skorohod , A . ( see Kostyučenko , A . ) Slobodyanski , M . G . 1 . On estimates for

the eigenvalues of a self - adjoint operator . Akad . Nauk SSSR . Prikl . Mat . Meh .

Weak compactness in

**Banach**spaces . Studia Math . 11 , 71 - 94 ( 1950 ) .Skorohod , A . ( see Kostyučenko , A . ) Slobodyanski , M . G . 1 . On estimates for

the eigenvalues of a self - adjoint operator . Akad . Nauk SSSR . Prikl . Mat . Meh .

Page 1869

Proof of a theorem of Thorin . Bull . Amer . Math . Soc . 50 , 279 - 282 ( 1944 ) .

Taylor , A . E . ( see also Bochner , S . ) 1 . The extension of linear functionals .

Duke Math . J . 5 , 538 - 547 ( 1939 ) . 2 . The weak topologies of

Proof of a theorem of Thorin . Bull . Amer . Math . Soc . 50 , 279 - 282 ( 1944 ) .

Taylor , A . E . ( see also Bochner , S . ) 1 . The extension of linear functionals .

Duke Math . J . 5 , 538 - 547 ( 1939 ) . 2 . The weak topologies of

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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