Linear Operators: General theory |
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Page 58
... continuous . By Theorem 2 , it is a homeomorphism , and so t1 = T2 . Q.E.D. 6 DEFINITION . A family F of functions which map one vector space into another vector space is called total if x = 0 is the only vector in X for which f ( x ) ...
... continuous . By Theorem 2 , it is a homeomorphism , and so t1 = T2 . Q.E.D. 6 DEFINITION . A family F of functions which map one vector space into another vector space is called total if x = 0 is the only vector in X for which 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
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
Copyright | |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets Cauchy sequence closed sets compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense disjoint Doklady Akad E₁ elements ergodic exists f₁ finite number follows function defined function f Hausdorff space Hence Hilbert space homomorphism integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz Russian S₁ scalar semi-group sequentially compact Show subset subspace Suppose Theorem theory topological space u-integrable u-measurable u-null uniformly unit sphere vector space weakly compact zero ΕΕΣ