## Linear Operators, Part 1 |

### From inside the book

Results 1-3 of 88

Page 34

The binary operation u is often written as u ( a , b ) = ab , and , when this notation

is used , it is

. The product ab is required to satisfy the following conditions : ( i ) a ( bc ) ...

The binary operation u is often written as u ( a , b ) = ab , and , when this notation

is used , it is

**called**multiplication . The element ab is**called**the product of a and b. The product ab is required to satisfy the following conditions : ( i ) a ( bc ) ...

Page 35

A one - to - one homomorphism is

isomorphism and if h ( A ) = B , then A and B are said to be isomorphic , or A is

said to be isomorphic with B. An isomorphism of a group G with itself is

...

A one - to - one homomorphism is

**called**an isomorphism . If h : A → B is anisomorphism and if h ( A ) = B , then A and B are said to be isomorphic , or A is

said to be isomorphic with B. An isomorphism of a group G with itself is

**called**an...

Page 38

Since there is a one - to - one linear map between the spaces M ; and Xin the

space X is often

the vector space X over the field Ø , the factor space X / M is the set of cosets of M

...

Since there is a one - to - one linear map between the spaces M ; and Xin the

space X is often

**called**the direct sum of the spaces X , . Xn . If M is a subspace ofthe vector space X over the field Ø , the factor space X / M is the set of cosets of M

...

### 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 | |

80 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

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