Linear Operators: General theory |
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Page 238
... is called n - dimensional unitary space , or n - dimensional Hilbert space . 2 The space is defined for positive integers n and real num- bers p with 1 ≤ p < ∞ . It 238 IV.2.1 IV . SPECIAL SPACES A List of Special Spaces •
... is called n - dimensional unitary space , or n - dimensional Hilbert space . 2 The space is defined for positive integers n and real num- bers p with 1 ≤ p < ∞ . It 238 IV.2.1 IV . SPECIAL SPACES A List of Special Spaces •
Page 782
... unitary operators . Mat . Sbornik N. S. 26 ( 68 ) , 247-264 ( 1950 ) . ( Russian ) Math . Rev. 11 , 669 ( 1950 ) . 2 . 3 . 4 . 5 . On the reduction of a linear non - Hermitian operator to " triangular " form . Doklady Akad . Nauk SSSR ...
... unitary operators . Mat . Sbornik N. S. 26 ( 68 ) , 247-264 ( 1950 ) . ( Russian ) Math . Rev. 11 , 669 ( 1950 ) . 2 . 3 . 4 . 5 . On the reduction of a linear non - Hermitian operator to " triangular " form . Doklady Akad . Nauk SSSR ...
Page 817
... unitary spaces . Proc . Nat . Acad . Sci . U.S.A. 28 , 170-175 ( 1942 ) . Generalized inverses of unbounded operators between two unitary spaces . Doklady Akad . Nauk SSSR ( N. S. ) 67 , 431-434 ( 1949 ) . ( Russian ) Math . Rev. 11 ...
... unitary spaces . Proc . Nat . Acad . Sci . U.S.A. 28 , 170-175 ( 1942 ) . Generalized inverses of unbounded operators between two unitary spaces . Doklady Akad . Nauk SSSR ( N. S. ) 67 , 431-434 ( 1949 ) . ( Russian ) Math . Rev. 11 ...
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