Linear Operators: General theory |
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Page 263
... arbitrary subset of S and F1 ranges over the closed subsets of E it follows from the preceding inequality that ( i ) μ2 ( E ) ≤μ2 ( EF ) + μ2 ( E — F ) . It will next be shown that for an arbitrary set E in S and an arbitrary closed ...
... arbitrary subset of S and F1 ranges over the closed subsets of E it follows from the preceding inequality that ( i ) μ2 ( E ) ≤μ2 ( EF ) + μ2 ( E — F ) . It will next be shown that for an arbitrary set E in S and an arbitrary closed ...
Page 476
... arbitrary finite subset of X , and ɛ > 0 is arbitrary . Thus , in the strong topology , a generalized sequence { T } converges to T if and only if { T } converges to Tx for every x in X. 3 DEFINITION . The weak operator topology in B ...
... arbitrary finite subset of X , and ɛ > 0 is arbitrary . Thus , in the strong topology , a generalized sequence { T } converges to T if and only if { T } converges to Tx for every x in X. 3 DEFINITION . The weak operator topology in B ...
Page 741
... arbitrary even order with variable coefficients . Proc . Nat . Acad . Sci . U.S.A. 38 , 230–235 ( 1952 ) . 2. The Dirichlet and vibration problems for linear elliptic differential equations of arbitrary order . Proc . Nat . Acad . Sci ...
... arbitrary even order with variable coefficients . Proc . Nat . Acad . Sci . U.S.A. 38 , 230–235 ( 1952 ) . 2. The Dirichlet and vibration problems for linear elliptic differential equations of arbitrary order . Proc . Nat . Acad . Sci ...
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