Linear Operators: General theory |
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Page 38
... of R is called a right ideal of R if it has the additional properties ( a ) Ix CI , x € R ; ( b ) ( 0 ) 1R . The definition of left ideal is similar . If I is both a right and a left ideal of R it is called a two - sided ideal . The ...
... of R is called a right ideal of R if it has the additional properties ( a ) Ix CI , x € R ; ( b ) ( 0 ) 1R . The definition of left ideal is similar . If I is both a right and a left ideal of R it is called a two - sided ideal . The ...
Page 39
... of R has an inverse , so R is a field . A right ( left , or two - sided ) ideal in a ring R is called a maximal right ( left , or two - sided ) ideal , if it is contained in no other ideal of the same type . If R contains a unit element ...
... of R has an inverse , so R is a field . A right ( left , or two - sided ) ideal in a ring R is called a maximal right ( left , or two - sided ) ideal , if it is contained in no other ideal of the same type . If R contains a unit element ...
Page 710
... R ( u ; T ) exists and equals ( I — R ( μ ; V ) K ) −1R ( u ; V ) . This follows from the identity R ( μ ; V ) ( uI ... of R ( μ ; V ) K . It follows from Lemma VII.6.13 that ( I - R ( u ; V ) K ) -1 exists and is an analytic function ...
... R ( u ; T ) exists and equals ( I — R ( μ ; V ) K ) −1R ( u ; V ) . This follows from the identity R ( μ ; V ) ( uI ... of R ( μ ; V ) K . It follows from Lemma VII.6.13 that ( I - R ( u ; V ) K ) -1 exists and is an analytic function ...
Contents
A Settheoretic Preliminaries | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets Cauchy sequence compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense differential equations disjoint Doklady Akad domain E₁ element exists f₁ finite dimensional finite number function defined function f Hausdorff space Hence Hilbert space homeomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field open set operator topology positive measure space Proc PROOF proved real numbers Riesz Russian S₁ scalar semi-group sequentially compact Show spectral strong operator topology subset subspace Suppose T₁ theory topological space u-integrable u-measurable uniformly unit sphere valued function weakly compact zero ΕΕΣ