Linear Operators: General theory |
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Page 458
... values 0 and 1. Show that { f } is a weak Cauchy sequence if and only if it ... boundary point of the closed unit sphere S of a B - space X is an extremal ... boundary point . But K has a continuous tangent functional at [ ] if and only ...
... values 0 and 1. Show that { f } is a weak Cauchy sequence if and only if it ... boundary point of the closed unit sphere S of a B - space X is an extremal ... boundary point . But K has a continuous tangent functional at [ ] if and only ...
Page 737
... values in a Banach space . Trans . Amer . Math . Soc . 38 , 357-378 ( 1935 ) . 5 . A note on topological groups . Compositio Math . 3 , 427–430 ( 1936 ) ... Boundary value and expansion problems of ordinary linear differential REFERENCES 737.
... values in a Banach space . Trans . Amer . Math . Soc . 38 , 357-378 ( 1935 ) . 5 . A note on topological groups . Compositio Math . 3 , 427–430 ( 1936 ) ... Boundary value and expansion problems of ordinary linear differential REFERENCES 737.
Page 763
... boundary value problems . Amer . J. Math . 70 , 847-855 ( 1948 ) . 2. The gaps in the essential spectra of wave equations . Amer . J. Math . 72 , 849-862 ( 1950 ) . Hartman , P. , and Wintner , A. 1. The ( L2 ) -space of relative ...
... boundary value problems . Amer . J. Math . 70 , 847-855 ( 1948 ) . 2. The gaps in the essential spectra of wave equations . Amer . J. Math . 72 , 849-862 ( 1950 ) . Hartman , P. , and Wintner , A. 1. The ( L2 ) -space of relative ...
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