## Linear Operators: General theory |

### From inside the book

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Page 36

A linear

group X together with an operation m : 0 X X -> X, written as m(a, x) = <xx, which

satisfy the following four conditions: (i) a.{x+y) = ctx+cty, cce0, x,ye£; The

elements ...

A linear

**vector space**, linear space, or**vector space**over a field 0 is an additivegroup X together with an operation m : 0 X X -> X, written as m(a, x) = <xx, which

satisfy the following four conditions: (i) a.{x+y) = ctx+cty, cce0, x,ye£; The

elements ...

Page 37

If T : X -»□ 3) and U : 2) -> 3 are linear transformations, and X, Q are linear

spaces over the same field 0, the product ... If X is a

is a scalar, the symbol clA is written for the set of elements of the form <xx with x

in A.

If T : X -»□ 3) and U : 2) -> 3 are linear transformations, and X, Q are linear

spaces over the same field 0, the product ... If X is a

**vector space**, if A Q X, and if ais a scalar, the symbol clA is written for the set of elements of the form <xx with x

in A.

Page 394

Ordered spaces. There is a vast literature dealing with

also assumed to possess an additional structure of order. For example, a partially

ordered

Ordered spaces. There is a vast literature dealing with

**vector spaces**which arealso assumed to possess an additional structure of order. For example, a partially

ordered

**vector space**is a**vector space**S3 in which there is defined a relation x ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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