Linear Operators: General theory |
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Page 46
... equal to the cardinality of B and if the cardinality of B is at most . equal to the cardinality of A , then these two sets have the same cardinality . ) 3 If X is a vector space over Ø , 46 I.14.1 I. PRELIMINARY CONCEPTS Exercises ·
... equal to the cardinality of B and if the cardinality of B is at most . equal to the cardinality of A , then these two sets have the same cardinality . ) 3 If X is a vector space over Ø , 46 I.14.1 I. PRELIMINARY CONCEPTS Exercises ·
Page 575
... equal to zero for μ in a neighborhood of σ , and equal to ( 2 — μ ) -1 for μ in a neighbor- hood of the remaining points of o ( T ) . Then g ( T ) ( λI —T ) = ( 21 — T ) g ( T ) = I - E ( o ) . If we define A1 : X → X by Д1x = X by Ax ...
... equal to zero for μ in a neighborhood of σ , and equal to ( 2 — μ ) -1 for μ in a neighbor- hood of the remaining points of o ( T ) . Then g ( T ) ( λI —T ) = ( 21 — T ) g ( T ) = I - E ( o ) . If we define A1 : X → X by Д1x = X by Ax ...
Page 716
... equal to one . Also the function identically equal to one is left fixed by T , so 1 € σ ( T ) . In the study of such processes one makes additional hypotheses on P which will guarantee that there exists an integer n and a compact ...
... equal to one . Also the function identically equal to one is left fixed by T , so 1 € σ ( T ) . In the study of such processes one makes additional hypotheses on P which will guarantee that there exists an integer n and a compact ...
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