## Linear Operators, Part 1 |

### From inside the book

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Page 776

Nelson Dunford, Jacob T. Schwartz. 3 . Some properties of a completely

continuous operator in Hilbert space . Latvijas PSR Zinātnu Akad . Vēstis 1950

no . 10 ( 39 ) , 93 - 106 ( 1950 ) . (

440 ( 1954 ) ...

Nelson Dunford, Jacob T. Schwartz. 3 . Some properties of a completely

continuous operator in Hilbert space . Latvijas PSR Zinātnu Akad . Vēstis 1950

no . 10 ( 39 ) , 93 - 106 ( 1950 ) . (

**Russian**. Latvian summary ) Math . Rev . 15 ,440 ( 1954 ) ...

Page 777

(

theory . Mat . Sbornik N . S . 33 ( 75 ) , 597 - 626 ( 1953 ) . (

15 , 720 ( 1954 ) . The theory of self - adjoint extensions of semi - bounded ...

(

**Russian**) Math . Rev . 11 , 670 ( 1950 ) . On the trace formula in perturbationtheory . Mat . Sbornik N . S . 33 ( 75 ) , 597 - 626 ( 1953 ) . (

**Russian**) Math . Rev .15 , 720 ( 1954 ) . The theory of self - adjoint extensions of semi - bounded ...

Page 794

Self - adjoint extensions of the second kind of a symmetric operator . Izvestiya

Akad . Nauk SSSR 4 , 53 – 104 ( 1940 ) . (

Rev . 2 , 104 ( 1941 ) . 8 . Spectral functions of a symmetric operator . Izvestiya

Akad .

Self - adjoint extensions of the second kind of a symmetric operator . Izvestiya

Akad . Nauk SSSR 4 , 53 – 104 ( 1940 ) . (

**Russian**. English summary ) Math .Rev . 2 , 104 ( 1941 ) . 8 . Spectral functions of a symmetric operator . Izvestiya

Akad .

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

25 other sections not shown

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### Common terms and phrases

algebra Amer analytic applied arbitrary assumed B-space Banach spaces bounded called clear closed compact operator complex condition Consequently constant contains continuous functions converges convex convex set Corollary countably additive defined DEFINITION denote dense determined differential dimensional disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows formula function defined function f given Hence Hilbert space identity implies inequality integral interval Lebesgue Lemma limit linear functional linear operator linear space Math neighborhood norm obtained operator operator topology problem projection PROOF properties proved range reflexive representation respect satisfies scalar seen semi-group separable sequence set function Show shown statement subset subspace sufficient Suppose Theorem theory topology u-measurable uniform uniformly unique unit sphere valued vector weak weakly compact zero