Linear Operators: General theory |
From inside the book
Results 1-3 of 83
Page 77
... converges . 48 Show that ∞ .. Σα = lim Σαπ n = 1 h → 0 n = 1 ' sin nh \ nh whenever k > 1 and the series on the left converges . b = { b } be two se- m Σn - o 49 ( Schur - Mertens ) . Let a = { a } and quences of complex numbers , and ...
... converges . 48 Show that ∞ .. Σα = lim Σαπ n = 1 h → 0 n = 1 ' sin nh \ nh whenever k > 1 and the series on the left converges . b = { b } be two se- m Σn - o 49 ( Schur - Mertens ) . Let a = { a } and quences of complex numbers , and ...
Page 145
... converges μ - uniformly if for each ɛ > 0 there is a set E € Σ such that vu , E ) < & and such that { f } converges uniformly on S - E . The sequence { f } converges u - uniformly to the function f if for each & > 0 there is a set E e Σ ...
... converges μ - uniformly if for each ɛ > 0 there is a set E € Σ such that vu , E ) < & and such that { f } converges uniformly on S - E . The sequence { f } converges u - uniformly to the function f if for each & > 0 there is a set E e Σ ...
Page 281
... converges at every point of A to a continuous limit fo . Then { f } converges to fo at every point of S if and only if { f } and every subsequence of { f } converges to fo quasi - uniformly on A. PROOF . Theorem 11 implies that the ...
... converges at every point of A to a continuous limit fo . Then { f } converges to fo at every point of S if and only if { f } and every subsequence of { f } converges to fo quasi - uniformly on A. PROOF . Theorem 11 implies that the ...
Contents
A Settheoretic Preliminaries | 1 |
10 | 30 |
Three Basic Principles of Linear Analysis | 49 |
Copyright | |
31 other sections not shown
Other editions - View all
Common terms and phrases
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