Linear Operators: General theory |
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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 ... HILBERT SPACE Hilbert Space.
... 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 ... HILBERT SPACE Hilbert Space.
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 ...
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 ba(S Banach spaces Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f g₁ Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear manifold linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ