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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 [ 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 .
Page 802
... Banach algebras with an adjoint operation . Ann . of Math . ( 2 ) 47 , 528-550 ( 1946 ) . 7 . 8 . 9 . The uniqueness of norm problem in Banach algebras . Ann . of Math . ( 2 ) 51 , 615-628 ( 1950 ) . Representation of certain Banach ...
... Banach algebras with an adjoint operation . Ann . of Math . ( 2 ) 47 , 528-550 ( 1946 ) . 7 . 8 . 9 . The uniqueness of norm problem in Banach algebras . Ann . of Math . ( 2 ) 51 , 615-628 ( 1950 ) . Representation of certain Banach ...
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
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
Copyright | |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets Cauchy sequence closed sets compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense disjoint Doklady Akad E₁ elements ergodic exists f₁ finite number follows function defined function f Hausdorff space Hence Hilbert space homomorphism integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz Russian S₁ scalar semi-group sequentially compact Show subset subspace Suppose Theorem theory topological space u-integrable u-measurable u-null uniformly unit sphere vector space weakly compact zero ΕΕΣ