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Page 746
... Banach space . Trans . Amer . Math . Soc . 69 , 105–131 ( 1950 ) . Branch points of solutions of equations in Banach ... spaces . Duke Math . J. 8 , 763-770 ( 1941 ) . Reflexive Banach spaces not isomorphic to uniformly convex spaces ...
... Banach space . Trans . Amer . Math . Soc . 69 , 105–131 ( 1950 ) . Branch points of solutions of equations in Banach ... spaces . Duke Math . J. 8 , 763-770 ( 1941 ) . Reflexive Banach spaces not isomorphic to uniformly convex spaces ...
Page 768
... space . Jap . J. Math . 13 , 501-513 ( 1936 ) . Notes on Banach space , I. Differentiation of abstract functions . Proc . Imp . Acad . Tokyo 18 , 127-130 ( 1942 ) . Izumi , S. , and Sunouchi , G. 1. Notes on Banach space ( VI ) ...
... space . Jap . J. Math . 13 , 501-513 ( 1936 ) . Notes on Banach space , I. Differentiation of abstract functions . Proc . Imp . Acad . Tokyo 18 , 127-130 ( 1942 ) . Izumi , S. , and Sunouchi , G. 1. Notes on Banach space ( VI ) ...
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