Linear Operators: General theory |
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Page 243
... Hilbert space has been defined by a set of abstract axioms . It is noteworthy that some of the concrete spaces defined above satisfy these axioms , and hence are special cases of abstract Hilbert space . Thus , for instance , the n ...
... Hilbert space has been defined by a set of abstract axioms . It is noteworthy that some of the concrete spaces defined above satisfy these axioms , and hence are special cases of abstract Hilbert space . Thus , for instance , the n ...
Page 256
... space , the norm will be explicitly mentioned . If , however , each of the spaces X1 , . . . , X , are Hilbert spaces then it will always be understood , sometimes without explicit mention , that is the uniquely deter- mined Hilbert space ...
... space , the norm will be explicitly mentioned . If , however , each of the spaces X1 , . . . , X , are Hilbert spaces then it will always be understood , sometimes without explicit mention , that is the uniquely deter- mined Hilbert space ...
Page 851
... space , II.3.1 ( 59 ) Orthocomplement of a set in Hilbert space , definition , IV.4.3 ( 249 ) properties , IV.4.4 ( 249 ) , IV.4.18 ( 256 ) Orthogonal complement of a set in a normed space , II.4.17 ( 72 ) remarks on , ( 93 ) Orthogonal ...
... space , II.3.1 ( 59 ) Orthocomplement of a set in Hilbert space , definition , IV.4.3 ( 249 ) properties , IV.4.4 ( 249 ) , IV.4.18 ( 256 ) Orthogonal complement of a set in a normed space , II.4.17 ( 72 ) remarks on , ( 93 ) Orthogonal ...
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