Linear Operators: General theory |
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Page 38
... ideal is similar . If I is both a right and a left ideal of R it is called a two - sided ideal . The subrings ( 0 ) and R are frequently called trivial , or improper , ideals and all other ideals proper ideals . Condition ( a ) above ...
... ideal is similar . If I is both a right and a left ideal of R it is called a two - sided ideal . The subrings ( 0 ) and R are frequently called trivial , or improper , ideals and all other ideals proper ideals . Condition ( a ) above ...
Page 39
... ideal , if it is contained in no other ideal of the same type . If R contains a unit element e , than any right ideal I。 is contained in a maximal right ideal . To see this , let & be the collection of all right ideals in R which ...
... ideal , if it is contained in no other ideal of the same type . If R contains a unit element e , than any right ideal I。 is contained in a maximal right ideal . To see this , let & be the collection of all right ideals in R which ...
Page 41
... ideal if and only if it is an algebraic ideal . If I is an ideal in a Boolean ring R , then R / I is a Boolean ring . Further , from the above we see that if M is a maximal ideal in a Boolean ring R with unit , then R / M is isomorphic ...
... ideal if and only if it is an algebraic ideal . If I is an ideal in a Boolean ring R , then R / I is a Boolean ring . Further , from the above we see that if M is a maximal ideal in a Boolean ring R with unit , then R / M is isomorphic ...
Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
Copyright | |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense disjoint Doklady Akad E₁ element ergodic exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear manifold linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ