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
A Settheoretic Preliminaries | 1 |
10 | 30 |
Three Basic Principles of Linear Analysis | 49 |
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A₁ additive set function algebra analytic arbitrary B-space B₁ ba(S Banach Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense E₁ element equation equivalent exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue measure Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space neighborhood non-negative non-zero normed linear space o-field o-finite open set operator topology positive measure space properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact X₁ zero ΕΕΣ