## Linear Operators: General theory |

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Page 802

The singular elements of a

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

– 464 ( 1950 ) . 6 .

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 ) . 6 .

**Banach**algebras with an adjoint operation . Ann . of Math .Page 810

Weak compactness in

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

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

Page 838

Ill special B-spaces, Chap. IV properties, IV.15 Baire category theorem, 1.6.9 (20)

convergence of measurable functions, IV. 11.2-3 (332-334)

theorem, ...

Ill special B-spaces, Chap. IV properties, IV.15 Baire category theorem, 1.6.9 (20)

**Banach**limits, existence and properties, II.4.22-23 (73)**Banach**theorem, onconvergence of measurable functions, IV. 11.2-3 (332-334)

**Banach**-Stonetheorem, ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

31 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 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