## Linear Operators, Part 1 |

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Page 34

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

used, it is called multiplication. The

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

b, ...

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) = (ab)&, a,

b, ...

Page 40

An

field, then a set X is said to be an algebra over p if X is a ring as well as a vector

space over Q) and if 2(aiy) = (xx)y= a(xy), a', ye X, o, e QP. A right (left, two-sided)

...

An

**element**which is not (right, left) regular is called (right, left) singular. If p is afield, then a set X is said to be an algebra over p if X is a ring as well as a vector

space over Q) and if 2(aiy) = (xx)y= a(xy), a', ye X, o, e QP. A right (left, two-sided)

...

Page 335

Let L be a q-complete lattice in which every set of

ordered under the partial ordering of L is at ... between

mean that a C b and that each

bound for a.

Let L be a q-complete lattice in which every set of

**elements**of L which is well-ordered under the partial ordering of L is at ... between

**elements**a, b in W tomean that a C b and that each

**element**a which is in b but not a is an upperbound for a.

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### Contents

A Settheoretic Preliminaries | 1 |

Convergence and Uniform Convergence of Generalized | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

27 other sections not shown

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