Linear Operators: General theory |
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Page 555
... unitary space leads to a rather complete description of the analytic behavior of the operator and , at the same time , furnishes a clear geometric picture of the manner in which the operator transforms the unitary space upon which it ...
... unitary space leads to a rather complete description of the analytic behavior of the operator and , at the same time , furnishes a clear geometric picture of the manner in which the operator transforms the unitary space upon which it ...
Page 728
... unitary operators in L2 ( S ) . Von Neumann's proof was based on the spectral theory of unitary operators in Hilbert space . Many exten- sions and generalizations of this ergodic theorem have been given , both to more general B - spaces ...
... unitary operators in L2 ( S ) . Von Neumann's proof was based on the spectral theory of unitary operators in Hilbert space . Many exten- sions and generalizations of this ergodic theorem have been given , both to more general B - spaces ...
Page 817
... unitary spaces . Proc . Nat . Acad . Sci . U.S.A. 28 , 170-175 ( 1942 ) . 2 . 3 . Generalized inverses of unbounded operators between two unitary spaces . Doklady Akad . Nauk SSSR ( N. S. ) 67 , 431-434 ( 1949 ) . ( Russian ) Math . Rev ...
... unitary spaces . Proc . Nat . Acad . Sci . U.S.A. 28 , 170-175 ( 1942 ) . 2 . 3 . Generalized inverses of unbounded operators between two unitary spaces . Doklady Akad . Nauk SSSR ( N. S. ) 67 , 431-434 ( 1949 ) . ( Russian ) Math . Rev ...
Contents
Preliminary Concepts | 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 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 ergodic exists f₁ finite dimensional function defined function f 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-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ