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 X into another vector space Y is called total if x = O 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 X into another vector space Y is called total if x = O 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
A Settheoretic Preliminaries | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets Cauchy sequence compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense differential equations disjoint Doklady Akad domain E₁ element exists f₁ finite dimensional finite number function defined function f Hausdorff space Hence Hilbert space homeomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field open set operator topology positive measure space Proc PROOF proved real numbers Riesz Russian S₁ scalar semi-group sequentially compact Show spectral strong operator topology subset subspace Suppose T₁ theory topological space u-integrable u-measurable uniformly unit sphere valued function weakly compact zero ΕΕΣ