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 X 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 X 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
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
Copyright | |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets Cauchy sequence closed sets compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense disjoint Doklady Akad E₁ elements ergodic exists f₁ finite number follows function defined function f Hausdorff space Hence Hilbert space homomorphism integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz Russian S₁ scalar semi-group sequentially compact Show subset subspace Suppose Theorem theory topological space u-integrable u-measurable u-null uniformly unit sphere vector space weakly compact zero ΕΕΣ