## Linear Operators: Spectral theory |

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Page 1797

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873 ( 1941 ) . 3 . Symmetric transformations in Hilbert space .

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**Math**. Soc . 45 , 369 - 442 ( 1939 ) . 2 . Two sided ideals and congruencesin the ring of bounded operators in Hilbert space . Ann . of

**Math**. ( 2 ) 42 , 839 –873 ( 1941 ) . 3 . Symmetric transformations in Hilbert space .

**Duke**J .**Math**.Page 1851

Math . Zeit . 37 , 647 – 668 ( 1933 ) . Parker , W . V . 1 . Limits to the characteristic

roots of a matrix .

theory of nuclear forces . Interscience Pub . , New York , 1946 . Peano , G . 1 .

Math . Zeit . 37 , 647 – 668 ( 1933 ) . Parker , W . V . 1 . Limits to the characteristic

roots of a matrix .

**Duke Math**. J . 10 , 479 - 482 ( 1943 ) . Pauli , W . 1 . Mesontheory of nuclear forces . Interscience Pub . , New York , 1946 . Peano , G . 1 .

Page 1876

Math . Ann . 68 , 220 - 269 ( 1910 ) . Almost periodic invariant vector sets in a

metric vector space . Amer . J . Math . 71 , 178 ... Math . - Phys . Kl . 1910 , 442 -

467 ( 1910 ) . 9 . The method of orthogonal projection in potential theory .

Math . Ann . 68 , 220 - 269 ( 1910 ) . Almost periodic invariant vector sets in a

metric vector space . Amer . J . Math . 71 , 178 ... Math . - Phys . Kl . 1910 , 442 -

467 ( 1910 ) . 9 . The method of orthogonal projection in potential theory .

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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