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Page 462
... Banach [ 1 ; pp . 58 , 134 ] . Mazur 1 ; p . 80 ] showed that a strongly closed convex set in a normed linear space contains all the weak limits of sequences in the set . His proof requires only minor changes to yield Theorem 3.13 . Banach ...
... Banach [ 1 ; pp . 58 , 134 ] . Mazur 1 ; p . 80 ] showed that a strongly closed convex set in a normed linear space contains all the weak limits of sequences in the set . His proof requires only minor changes to yield Theorem 3.13 . Banach ...
Page 802
... Banach algebras with an adjoint operation . Ann . of Math . ( 2 ) 47 , 528-550 ( 1946 ) . 7 . 8 . 9 . 10 . The uniqueness of norm problem in Banach algebras . Ann . of Math . ( 2 ) 51 , 615-628 ( 1950 ) . Representation of certain ...
... Banach algebras with an adjoint operation . Ann . of Math . ( 2 ) 47 , 528-550 ( 1946 ) . 7 . 8 . 9 . 10 . The uniqueness of norm problem in Banach algebras . Ann . of Math . ( 2 ) 51 , 615-628 ( 1950 ) . Representation of certain ...
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 ...
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 B₁ ba(S Banach spaces Borel sets Cauchy sequence compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense differential equations disjoint Doklady Akad domain E₁ element exists f₁ finite dimensional finite number function defined function f Hausdorff space Hence Hilbert space homeomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field open set operator topology positive measure space Proc PROOF proved real numbers Riesz Russian S₁ scalar semi-group sequentially compact Show spectral strong operator topology subset subspace Suppose T₁ theory topological space u-integrable u-measurable uniformly unit sphere valued function weakly compact zero ΕΕΣ