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 247
... Hilbert Space Of the infinite dimensional B - spaces , Hilbert space is the most closely related , especially in its elementary geometrical aspects , to the Euclidean or finite dimensional unitary spaces . It is not immediate from the ...
... Hilbert Space Of the infinite dimensional B - spaces , Hilbert space is the most closely related , especially in its elementary geometrical aspects , to the Euclidean or finite dimensional unitary spaces . It is not immediate from the ...
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 ...
Contents
B Topological Preliminaries | 10 |
Metric Spaces | 23 |
Product Spaces | 31 |
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 compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense differential equations Doklady Akad Duke Math E₁ elements ergodic exists extension f₁ function defined function f Hausdorff space Hence Hilbert space homomorphism inequality 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 o-field 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 theory topological space u-integrable u-measurable u-null uniformly unit sphere valued function vector space weakly compact zero ΕΕΣ