## Linear Operators: General theory |

### From inside the book

Results 1-3 of 85

Page 373

This generalizes and abstracts a result

1] by E. Fischer [2]. The fact that a linear manifold which is not dense in the entire

space has a non-zero orthogonal complement (

This generalizes and abstracts a result

**proved**for closed linear manifolds in L2[0,1] by E. Fischer [2]. The fact that a linear manifold which is not dense in the entire

space has a non-zero orthogonal complement (

**proved**in 4.4) was**proved**...Page 385

We now comment briefly on the Theorems 6.18 — 6.27. They are essentially due,

at least in the real case, to Stone [1], although his terminology and proofs often

differ from that given here. It should be mentioned that Theorem 6.22 was

...

We now comment briefly on the Theorems 6.18 — 6.27. They are essentially due,

at least in the real case, to Stone [1], although his terminology and proofs often

differ from that given here. It should be mentioned that Theorem 6.22 was

**proved**...

Page 462

116]. Dieudonne' [3; p. 109]

induction. The case of Theorem 3.9 in which H — ?)* and T = VJ), was

the separable case by Banach [1; p. 131] and in full generality by Alaoglu [1; p.

256].

116]. Dieudonne' [3; p. 109]

**proved**3.9 after establishing Lemma 3.10 byinduction. The case of Theorem 3.9 in which H — ?)* and T = VJ), was

**proved**inthe separable case by Banach [1; p. 131] and in full generality by Alaoglu [1; p.

256].

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries 84 | 34 |

Copyright | |

80 other sections not shown

### Other editions - View all

### Common terms and phrases

a-finite Acad additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear functional convex set Corollary countably additive Definition denote dense Doklady Akad element equivalent everywhere exists finite dimensional follows from Theorem function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral interval isometric isomorphism Lebesgue measure linear map linear operator linear topological space LP(S measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative non-zero normed linear space open set operator topology positive measure space Proc properties proved real numbers reflexive Riesz Russian scalar semi-group sequentially compact Show simple functions subset subspace Suppose theory TM(S topological space valued function vector space weak topology weakly compact weakly sequentially compact zero