Linear Operators: General theory |
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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
... Banachschen Räumen . Doklady Akad . Nauk SSSR ( N. S. ) 28 , 199-202 ( 1940 ) . 3. Weak compactness in Banach spaces . Studia Math . 11 , 71-94 ( 1950 ) . Skorohod , A. ( see Kostyučenko , A. ) Slobodyanskii , M. G. 1. On estimates for ...
... Banachschen Räumen . Doklady Akad . Nauk SSSR ( N. S. ) 28 , 199-202 ( 1940 ) . 3. Weak compactness in Banach spaces . Studia Math . 11 , 71-94 ( 1950 ) . Skorohod , A. ( see Kostyučenko , A. ) Slobodyanskii , M. G. 1. On estimates for ...
Page 815
... Banach spaces . Revista Ci . , Lima 42 , 355–366 ( 1940 ) ; 43 , 465-474 ( 1941 ) ; 44 , 45–63 ( 1942 ) . 3. The weak topologies of Banach spaces . Proc . Nat . Acad . Sci . U.S.A. 25 , 438-440 ( 1939 ) . 4 . 6 . On certain Banach ...
... Banach spaces . Revista Ci . , Lima 42 , 355–366 ( 1940 ) ; 43 , 465-474 ( 1941 ) ; 44 , 45–63 ( 1942 ) . 3. The weak topologies of Banach spaces . Proc . Nat . Acad . Sci . U.S.A. 25 , 438-440 ( 1939 ) . 4 . 6 . On certain Banach ...
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