Linear Operators: General theory |
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Page 13
... inverse function ƒ - 1 is also continuous , then f is called a homeomorphism , or a topological iso- morphism . In this situation , the spaces X and Y are said to be homeo- morphic . 16 LEMMA . Let X , Y be topological spaces and let f ...
... inverse function ƒ - 1 is also continuous , then f is called a homeomorphism , or a topological iso- morphism . In this situation , the spaces X and Y are said to be homeo- morphic . 16 LEMMA . Let X , Y be topological spaces and let f ...
Page 592
... inverse for no point in D or else this inverse exists except at a countable number of isolated points . PROOF . If λ € D is such that T - 1 ( 26 ) exists , then it follows from Lemma 6 that for 2 sufficiently near 2 the inverse T - 1 ...
... inverse for no point in D or else this inverse exists except at a countable number of isolated points . PROOF . If λ € D is such that T - 1 ( 26 ) exists , then it follows from Lemma 6 that for 2 sufficiently near 2 the inverse T - 1 ...
Page 847
... Inverse function and inverse image , ( 3 ) Inverse of an operator and adjoints , VI.2.7 ( 479 ) existence and continuity of , VII.6.1 ( 584 ) Inverting sequence of polynomials , VIII.2.12 ( 650 ) Involution , in an algebra , ( 40 ) ...
... Inverse function and inverse image , ( 3 ) Inverse of an operator and adjoints , VI.2.7 ( 479 ) existence and continuity of , VII.6.1 ( 584 ) Inverting sequence of polynomials , VIII.2.12 ( 650 ) Involution , in an algebra , ( 40 ) ...
Contents
Preliminary Concepts | 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 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 ergodic exists f₁ finite dimensional function defined function f 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-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ