Linear Operators, Part 1 |
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Page 188
Q.E.D. As in the case of finite measure spaces we shall call the measure space (
S, 2, u) constructed in Corollary 6 from the g-finite measure spaces (S, 2, u,) the
product measure space and write (S, 2, u) = P-1 (S1, 2, u). The best known ...
Q.E.D. As in the case of finite measure spaces we shall call the measure space (
S, 2, u) constructed in Corollary 6 from the g-finite measure spaces (S, 2, u,) the
product measure space and write (S, 2, u) = P-1 (S1, 2, u). The best known ...
Page 246
8 CoRollary. A finite dimensional normed linear space is reflerive. - PRoof. In the
notation of Corollary 7, n n wor = X boCo)"(b), w” = X bow”(b.), 7–1 f=1 - and thus
for w” in *** we have wor” – wor, where r =X; i wo (bo)b,. Q.E.D. From Corollary ...
8 CoRollary. A finite dimensional normed linear space is reflerive. - PRoof. In the
notation of Corollary 7, n n wor = X boCo)"(b), w” = X bow”(b.), 7–1 f=1 - and thus
for w” in *** we have wor” – wor, where r =X; i wo (bo)b,. Q.E.D. From Corollary ...
Page 422
Conversely, if Q) is T-closed and a g \), then, by Corollary 2.12, there is a 1'-
continuous fo and a constant c such that %fo()) < c, fo(a) # 0. By Lemma 1.11, fo
()) = 0; by Theorem 9, foe T. Put f = fo/fo(a), and the corollary is proved. Q.E.D. 13
...
Conversely, if Q) is T-closed and a g \), then, by Corollary 2.12, there is a 1'-
continuous fo and a constant c such that %fo()) < c, fo(a) # 0. By Lemma 1.11, fo
()) = 0; by Theorem 9, foe T. Put f = fo/fo(a), and the corollary is proved. Q.E.D. 13
...
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Contents
A Settheoretic Preliminaries | 1 |
Convergence and Uniform Convergence of Generalized | 26 |
Algebraic Preliminaries | 34 |
Copyright | |
27 other sections not shown
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Common terms and phrases
additive set function algebra Amer analytic arbitrary B-space Banach baſs Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complete complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense differential Doklady Akad element equation equivalent exists finite dimensional function defined function f g-field g-finite Hausdorff space Hence Hilbert space homeomorphism implies inequality integral interval isometric isomorphism Lebesgue measure Lemma Let f lim ſº linear map linear operator linear topological space Lp(S Math measurable functions measure space metric space Nauk SSSR N.S. neighborhood non-negative normed linear space open set operator topology positive measure space Proc properties proved real numbers Riesz 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 zero
Bibliographic information
| Title | Linear Operators, Part 1 Linear Operators, Nelson Dunford Volume 1 of Linear Operators: General Theory. Spectral Theory, Self Adjoint Operators in Hilbert Space. Spectral Operators. I. II. III, Jacob T. Schwartz Volume 7 of Pure and applied mathematics : a series of texts and monographs Pure and applied mathematics, ISSN 0079-8185 Wiley classics library |
| Authors | Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle |
| Edition | reprint |
| Publisher | Interscience Publishers, 1958 |
| Original from | the University of California |
| Digitized | 26 Jun 2018 |
| Length | 2592 pages |
| Export Citation | BiBTeX EndNote RefMan |