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 , T ” for T ” -1T . The symbol I is used for ...
... 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 , T ” for T ” -1T . The symbol I is used for ...
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
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