Linear Operators: General theory |
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Page 18
Subiman Kundu, Manisha Aggarwal. Evidently , in a metric space ( X , d ) , every non - empty subset of a bounded set in ( X , d ) is again bounded . In particular , we have Proposition 1.3.3 . Let ( X , d ) be a metric space and A be a ...
Subiman Kundu, Manisha Aggarwal. Evidently , in a metric space ( X , d ) , every non - empty subset of a bounded set in ( X , d ) is again bounded . In particular , we have Proposition 1.3.3 . Let ( X , d ) be a metric space and A be a ...
Page 74
Irving Kaplansky. THEOREM 31. A subset of a metric space is open if and only if it contains, along with any point x, some neighborhood of x. We conclude this section with two definitions. DEFINITION. A point x in a metric space is called ...
Irving Kaplansky. THEOREM 31. A subset of a metric space is open if and only if it contains, along with any point x, some neighborhood of x. We conclude this section with two definitions. DEFINITION. A point x in a metric space is called ...
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... spaces of different types: linear space with scalar product (4.1.7), pseudometric space (4.2.1), semimetric space (4.2.2), and l1 -metric space (4.2.3) are contained in the table 4.2.2. Notice, that a computational rate of performing ...
... spaces of different types: linear space with scalar product (4.1.7), pseudometric space (4.2.1), semimetric space (4.2.2), and l1 -metric space (4.2.3) are contained in the table 4.2.2. Notice, that a computational rate of performing ...
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