Linear Operators: General theory |
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Page 743
... Math . 78 , 282-288 ( 1956 ) . 4 . 5 . On the existence of certain singular integrals . Acta Math . 88 , 85–139 ( 1952 ) . On singular integrals . Amer . J. Math . 78 , 289–309 ( 1956 ) . 6. Algebras of certain singular operators . Amer . J ...
... Math . 78 , 282-288 ( 1956 ) . 4 . 5 . On the existence of certain singular integrals . Acta Math . 88 , 85–139 ( 1952 ) . On singular integrals . Amer . J. Math . 78 , 289–309 ( 1956 ) . 6. Algebras of certain singular operators . Amer . J ...
Page 763
... Math . 76 , 831-838 ( 1954 ) . Hartman , P. , and Putnam , C. 1. The least cluster point of the spectrum of boundary value problems . Amer . J. Math . 70 , 847-855 ( 1948 ) . 2. The gaps in the essential spectra of wave equations . Amer ...
... Math . 76 , 831-838 ( 1954 ) . Hartman , P. , and Putnam , C. 1. The least cluster point of the spectrum of boundary value problems . Amer . J. Math . 70 , 847-855 ( 1948 ) . 2. The gaps in the essential spectra of wave equations . Amer ...
Page 790
... Math . J. 5 , 520–534 ( 1939 ) . 2. On the supporting - plane property of a convex body . Bull . Amer . Math . Soc . 46 , 482-489 ( 1940 ) . Munroe , M. E. 1. Absolute and unconditional convergence in Banach spaces . Duke Math . J. 13 ...
... Math . J. 5 , 520–534 ( 1939 ) . 2. On the supporting - plane property of a convex body . Bull . Amer . Math . Soc . 46 , 482-489 ( 1940 ) . Munroe , M. E. 1. Absolute and unconditional convergence in Banach spaces . Duke Math . J. 13 ...
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