## Linear Operators: Spectral Theory : Self Adjoint Operators in Hilbert Space, Volume 2 |

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Page 2162

Spectral Theory : Self Adjoint Operators in Hilbert Space Nelson Dunford, Jacob

Theodore Schwartz. PROOF . If the bounded

complete space has properties ( B ) and ( G ) then , by Lemma 4 , it has

properties ( A ) ...

Spectral Theory : Self Adjoint Operators in Hilbert Space Nelson Dunford, Jacob

Theodore Schwartz. PROOF . If the bounded

**linear operator**T in a weaklycomplete space has properties ( B ) and ( G ) then , by Lemma 4 , it has

properties ( A ) ...

Page 2400

Spectral Theory : Self Adjoint Operators in Hilbert Space Nelson Dunford, Jacob

Theodore Schwartz. 2. ... Let X be a B - space , and let T be a

; let k be a second

Spectral Theory : Self Adjoint Operators in Hilbert Space Nelson Dunford, Jacob

Theodore Schwartz. 2. ... Let X be a B - space , and let T be a

**linear operator**in %; let k be a second

**linear operator**in x which is , in a sense to be made precise ...Page 2591

countably additive, XV.2 (1930), XV.2.3 (1930), XV.2.4 (1931) definition of, XV.2.1

(1929) integral with respect to, XV.2 (1929) Spectral

2148), XVI.5. 16 (2162) canonical reduction of, XV.4 (1937), XV.4.5 (1939), ...

countably additive, XV.2 (1930), XV.2.3 (1930), XV.2.4 (1931) definition of, XV.2.1

(1929) integral with respect to, XV.2 (1929) Spectral

**operator**, adjoint of, XVI.4.6 (2148), XVI.5. 16 (2162) canonical reduction of, XV.4 (1937), XV.4.5 (1939), ...

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### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

47 other sections not shown

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### Common terms and phrases

adjoint operator Amer analytic apply arbitrary assumed B-space Banach space belongs Boolean algebra Borel set boundary conditions bounded bounded operator Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding defined Definition denote dense determined differential operator discrete domain elements equation equivalent established exists extension fact finite follows formal formula function given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear operator Math Moreover multiplicity norm perturbation plane positive preceding present problem projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type seen sequence shown shows similar solution spectral measure spectral operator spectrum subset sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero