Linear Operators: General theory |
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Page 256
... Hilbert spaces then it will always be understood , sometimes without explicit mention , that is the uniquely deter- mined Hilbert space with scalar product n ( iv ) ( [ x1 , ... , xn ] , [ Y1 , • • • , Yn ] ) = Σ ( xi , Yi ) i , i = 1 ...
... Hilbert spaces then it will always be understood , sometimes without explicit mention , that is the uniquely deter- mined Hilbert space with scalar product n ( iv ) ( [ x1 , ... , xn ] , [ Y1 , • • • , Yn ] ) = Σ ( xi , Yi ) i , i = 1 ...
Page 814
... Hilbert space . Proc . Nat . Acad . Sci . U.S.A. 24 , 559-560 ( 1938 ) . On uniformly bounded linear transformations in Hilbert space . Acta Sci . Math . Szeged 11 , 152-157 ( 1947 ) . Sur les contractions de l'espace de Hilbert . Acta ...
... Hilbert space . Proc . Nat . Acad . Sci . U.S.A. 24 , 559-560 ( 1938 ) . On uniformly bounded linear transformations in Hilbert space . Acta Sci . Math . Szeged 11 , 152-157 ( 1947 ) . Sur les contractions de l'espace de Hilbert . Acta ...
Page 851
... Hilbert space , IV.4.3 ( 249 ) Orthogonal projections in Hilbert spaces , IV.4.8 ( 250 ) Orthogonal series , exercises on , VI.11.43-47 ( 537 ) study of , IV.14 Orthonormal set in Hilbert space , closed set , IV.14.1 ( 357 ) complete ...
... Hilbert space , IV.4.3 ( 249 ) Orthogonal projections in Hilbert spaces , IV.4.8 ( 250 ) Orthogonal series , exercises on , VI.11.43-47 ( 537 ) study of , IV.14 Orthonormal set in Hilbert space , closed set , IV.14.1 ( 357 ) complete ...
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