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Page 245
Nelson Dunford, Jacob T. Schwartz. 3 COROLLARY . An n - dimensional B - space is equivalent to En . 4 COROLLARY . Every linear operator on a finite dimensional normed linear space is continuous . ... 9 ท PROOF . Let ( b1 , · b1 } be a ...
Nelson Dunford, Jacob T. Schwartz. 3 COROLLARY . An n - dimensional B - space is equivalent to En . 4 COROLLARY . Every linear operator on a finite dimensional normed linear space is continuous . ... 9 ท PROOF . Let ( b1 , · b1 } be a ...
Page 246
... dimension . Q.E.D. In the preceding lemma it is assumed that the spaces are normed linear spaces , for there are examples ( see the preliminary discussion in Section IV.11 ) of infinite dimensional F - spaces with zero dimensional ...
... dimension . Q.E.D. In the preceding lemma it is assumed that the spaces are normed linear spaces , for there are examples ( see the preliminary discussion in Section IV.11 ) of infinite dimensional F - spaces with zero dimensional ...
Page 556
Nelson Dunford, Jacob T. Schwartz. 1. Spectral Theory in a Finite Dimensional Space Throughout this section , X will denote a finite dimensional com- plex B - space , and T a linear operator in B ( X ) . Our aim is to study the algebraic ...
Nelson Dunford, Jacob T. Schwartz. 1. Spectral Theory in a Finite Dimensional Space Throughout this section , X will denote a finite dimensional com- plex B - space , and T a linear operator in B ( X ) . Our aim is to study the algebraic ...
Contents
A Settheoretic Preliminaries | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f g₁ Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear manifold linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ