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Page 83
... Banach [ 7 ] ( see also Banach [ 1 ; Chap . 1 ] and Kuratowski [ 1 ] ) . Conditions of this nature are extended to polynomial operators by Mazur and Orlicz [ 2 ] . It is sometimes useful to define a notion of " continuity " of a li ...
... Banach [ 7 ] ( see also Banach [ 1 ; Chap . 1 ] and Kuratowski [ 1 ] ) . Conditions of this nature are extended to polynomial operators by Mazur and Orlicz [ 2 ] . It is sometimes useful to define a notion of " continuity " of a li ...
Page 85
... Banach did not initiate the study of these spaces , his contributions were many and deep - for that reason many authors use the term Banach space to refer to a complete normed linear space . Throughout this work , we will adhere more ...
... Banach did not initiate the study of these spaces , his contributions were many and deep - for that reason many authors use the term Banach space to refer to a complete normed linear space . Throughout this work , we will adhere more ...
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 |
10 | 30 |
Three Basic Principles of Linear Analysis | 49 |
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A₁ additive set function algebra analytic arbitrary B-space B₁ ba(S Banach Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense E₁ element equation equivalent exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue measure Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space neighborhood non-negative non-zero normed linear space o-field o-finite open set operator topology positive measure space properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact X₁ zero ΕΕΣ