Linear Operators: General theory |
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Page 10
... sets in 7 are called the open sets of ( X , t ) . A neighborhood of the point p is an open set containing p . A neighborhood of the set A is an open set containing 4. If A is a subset of X , then a point p is a limit point , or a point ...
... sets in 7 are called the open sets of ( X , t ) . A neighborhood of the point p is an open set containing p . A neighborhood of the set A is an open set containing 4. If A is a subset of X , then a point p is a limit point , or a point ...
Page 84
... open set onto a set whose closure contains an open set . Pettis [ 5 ] proved theorems extending some of the results of Banach [ 7 ] , Freudenthal [ 2 ] , and Lorentz [ 3 ] , and which , when spe- cialized to linear spaces , contain most ...
... open set onto a set whose closure contains an open set . Pettis [ 5 ] proved theorems extending some of the results of Banach [ 7 ] , Freudenthal [ 2 ] , and Lorentz [ 3 ] , and which , when spe- cialized to linear spaces , contain most ...
Page 213
... open set G of real Euclidean n - space En . Let 0 < r < ∞ . ( a ) If for each p in a set AC G 2 ( C ) lim inf 4 ( C ) → 0 м ( С ) < r , where C is a closed cube containing p , then each neighborhood of A con- tains an open set Q such ...
... open set G of real Euclidean n - space En . Let 0 < r < ∞ . ( a ) If for each p in a set AC G 2 ( C ) lim inf 4 ( C ) → 0 м ( С ) < r , where C is a closed cube containing p , then each neighborhood of A con- tains an open set Q such ...
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