## Linear Operators: General theory |

### From inside the book

Results 1-3 of 89

Page 50

( a ) In a topological group G , any algebraic combination of any number of

variables x1 , . . . Xn is continuous as a map of GX . . . XG into G . ( b ) In a linear

Come and ...

( a ) In a topological group G , any algebraic combination of any number of

variables x1 , . . . Xn is continuous as a map of GX . . . XG into G . ( b ) In a linear

**topological space**X , all linear combinations of any number of scalars dy , . .Come and ...

Page 413

non - zero linear functional on the complex space X , which separates the sets M

and N . Q . E . D . 2 . Linear

Section 1 are applied to linear

section ...

non - zero linear functional on the complex space X , which separates the sets M

and N . Q . E . D . 2 . Linear

**Topological Spaces**In this section , the results ofSection 1 are applied to linear

**topological spaces**. Statements 1 - 6 of thissection ...

Page 838

space of, definition, IV.2.24 (242) properties, IV.15 Annihilator of a set, II.4.17 (72)

Arzela theorem, on continuity of limit ... 1.11 (100) operator, definition, II.3.5 (60)

set in a linear

space of, definition, IV.2.24 (242) properties, IV.15 Annihilator of a set, II.4.17 (72)

Arzela theorem, on continuity of limit ... 1.11 (100) operator, definition, II.3.5 (60)

set in a linear

**topological space**, II.1.7 (51) criterion for boundedness in a ...### 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 | 34 |

Copyright | |

31 other sections not shown

### Other editions - View all

### 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