Linear Operators: General theory |
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Page 245
... finite dimensional normed linear space is continuous . = PROOF . Let { b1 , . . . , b1 } be a Hamel basis for the finite dimension- al normed linear space X so that every x in X has a unique represen- tation in the form x a11 + ... + ...
... finite dimensional normed linear space is continuous . = PROOF . Let { b1 , . . . , b1 } be a Hamel basis for the finite dimension- al normed linear space X so that every x in X has a unique represen- tation in the form x a11 + ... + ...
Page 246
... finite . Then the dimension of X ** is finite , and , since X is equivalent to a subspace of X ** ( II.3.19 ) , the ... dimensional F - spaces with zero dimensional conjugate spaces . The following corollary was established during the ...
... finite . Then the dimension of X ** is finite , and , since X is equivalent to a subspace of X ** ( II.3.19 ) , the ... dimensional F - spaces with zero dimensional conjugate spaces . The following corollary was established during the ...
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
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ 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 ergodic exists f₁ finite dimensional function defined function f 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-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ