## Linear Operators: General theory |

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Page 40

If / is a two-sided ideal in an

called the quotient

the linear space cases. A mapping of an

...

If / is a two-sided ideal in an

**algebra**X then the quotient ring X/I is an**algebra**,called the quotient

**algebra**, under the operations defined above in the ring andthe linear space cases. A mapping of an

**algebra**X into another**algebra**over the...

Page 44

On the other hand, if B is a Boolean ring with unit denoted by 1, then if x y is

defined to mean x = xy, and x' = 1 +x then B is a Boolean

xy, XAy = xy. Thus the concepts of Boolean

are ...

On the other hand, if B is a Boolean ring with unit denoted by 1, then if x y is

defined to mean x = xy, and x' = 1 +x then B is a Boolean

**algebra**and xvy = x+y+xy, XAy = xy. Thus the concepts of Boolean

**algebra**and Boolean ring with unitare ...

Page 272

We continue our analysis of the space C(S) with a discussion of certain important

special properties related to its structure as an

a well known approximation theorem of Weierstrass, which asserts that a ...

We continue our analysis of the space C(S) with a discussion of certain important

special properties related to its structure as an

**algebra**. One of these properties isa well known approximation theorem of Weierstrass, which asserts that a ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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a-field Acad additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets ca(S Cauchy sequence compact operator complex numbers complex valued contains continuous functions continuous linear convex set Corollary countably additive Definition denote dense differential equations disjoint sets Doklady Akad Duke Math element equivalent everywhere exists extended real valued extension finite dimensional finite number function f Hausdorff space Hence Hilbert space homeomorphism inequality interval Lebesgue measure lim sup linear functional linear map linear operator linear topological space LP(S measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space null set open set operator topology positive measure space Proc Proof properties proved real numbers Riesz Russian semi-group sequentially compact Show simple functions subset subspace Suppose theory topological space Trans uniformly unique v(fi valued function Vber vector valued weakly compact