Linear Operators: General theory |
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Page 14
... continuous , then the composite function fg is continu- ous . → The term scalar will be used for a real or complex ... functions on a topological space X , and let a be a scalar . Then the functions given by the expressions \ f ( x ) ...
... continuous , then the composite function fg is continu- ous . → The term scalar will be used for a real or complex ... functions on a topological space X , and let a be a scalar . Then the functions given by the expressions \ f ( x ) ...
Page 274
... continuous functions on S. Let A be a closed subalgebra of C ( S ) which contains the unit e and contains , with f ... functions in A. Then A , is a closed subalgebra containing the unit of the real algebra C , ( S ) of all real ...
... continuous functions on S. Let A be a closed subalgebra of C ( S ) which contains the unit e and contains , with f ... functions in A. Then A , is a closed subalgebra containing the unit of the real algebra C , ( S ) of all real ...
Page 381
... continuous functions on a locally compact Hausdorff space which vanish outside of compact sets . Arens [ 3 ] discussed certain sub - algebras of continuous functions on a topological space such that { s || f ( s ) | > c > 0 } is compact ...
... continuous functions on a locally compact Hausdorff space which vanish outside of compact sets . Arens [ 3 ] discussed certain sub - algebras of continuous functions on a topological space such that { s || f ( s ) | > c > 0 } is compact ...
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