Linear Operators: General theory |
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Page 37
... linear transformation which maps X into 3. If T is a linear operator on X to X , it is said to be a linear operator in X. For such operators the symbol T2 is used for TT , and , inductively , Tn for T - 1T . The symbol I is used for the ...
... linear transformation which maps X into 3. If T is a linear operator on X to X , it is said to be a linear operator in X. For such operators the symbol T2 is used for TT , and , inductively , Tn for T - 1T . The symbol I is used for the ...
Page 486
... operator topology of B ( X , Y ) . PROOF . Let S be the closed unit sphere in X , let T , be compact , and let T - T ... Linear combinations of compact linear operators are compact operators , and any product of a compact linear operator ...
... operator topology of B ( X , Y ) . PROOF . Let S be the closed unit sphere in X , let T , be compact , and let T - T ... Linear combinations of compact linear operators are compact operators , and any product of a compact linear operator ...
Page 494
... operator T , defined by ( b ) , is a bounded linear operator on C ( S ) to X whose adjoint T * is given by ( d ) . From IV.10.2 we conclude that T * maps the unit sphere of X * into a conditionally weakly compact set of rca ( S ) , and ...
... operator T , defined by ( b ) , is a bounded linear operator on C ( S ) to X whose adjoint T * is given by ( d ) . From IV.10.2 we conclude that T * maps the unit sphere of X * into a conditionally weakly compact set of rca ( S ) , and ...
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 ba(S Banach spaces Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f g₁ Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear manifold linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ