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Page 462
... Banach [ 1 ; p . 131 ] and in full generality by Alaoglu [ 1 ; p . 256 ] . Michael [ 1 ] gave an extension of Lemma 3.10 to a case where linear operators are considered . The equivalence of weak and strong closure for subspaces of a ...
... Banach [ 1 ; p . 131 ] and in full generality by Alaoglu [ 1 ; p . 256 ] . Michael [ 1 ] gave an extension of Lemma 3.10 to a case where linear operators are considered . The equivalence of weak and strong closure for subspaces of a ...
Page 804
... Banach spaces . Duke Math . J. 15 , 421-431 ( 1948 ) . 7. Mapping degree in Banach spaces and spectral theory . Math . Z. 63 , 195-218 ( 1955 ) . Rubin , H. , and Stone , M. H. 1 . Postulates for generalizations of Hilbert space . Proc ...
... Banach spaces . Duke Math . J. 15 , 421-431 ( 1948 ) . 7. Mapping degree in Banach spaces and spectral theory . Math . Z. 63 , 195-218 ( 1955 ) . Rubin , H. , and Stone , M. H. 1 . Postulates for generalizations of Hilbert space . Proc ...
Page 810
... Banach spaces . Studia Math . 11 , 71-94 ( 1950 ) . Skorohod , A. ( see Kostyučenko , A. ) Slobodyanskii , M. G. 1 ... Banach spaces . Doklady Akad . Nauk SSSR ( N. S. ) 22 , 471–473 ( 1939 ) . 2 . 3 . 4 . 5 . 6 . 7 . Sur les topologies ...
... Banach spaces . Studia Math . 11 , 71-94 ( 1950 ) . Skorohod , A. ( see Kostyučenko , A. ) Slobodyanskii , M. G. 1 ... Banach spaces . Doklady Akad . Nauk SSSR ( N. S. ) 22 , 471–473 ( 1939 ) . 2 . 3 . 4 . 5 . 6 . 7 . Sur les topologies ...
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