Linear Operators: General theory |
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Page 373
This generalizes and abstracts a result proved for closed linear manifolds in L2[0,
1] by E. Fischer [2]. The fact that a linear manifold which is not dense in the entire
space has a non-zero orthogonal complement (proved in 4.4) was proved ...
This generalizes and abstracts a result proved for closed linear manifolds in L2[0,
1] by E. Fischer [2]. The fact that a linear manifold which is not dense in the entire
space has a non-zero orthogonal complement (proved in 4.4) was proved ...
Page 385
We now comment briefly on the Theorems 6.18 — 6.27. They are essentially due,
at least in the real case, to Stone [1], although his terminology and proofs often
differ from that given here. It should be mentioned that Theorem 6.22 was proved
...
We now comment briefly on the Theorems 6.18 — 6.27. They are essentially due,
at least in the real case, to Stone [1], although his terminology and proofs often
differ from that given here. It should be mentioned that Theorem 6.22 was proved
...
Page 463
124] also proved that in the case of a separable space these notions coincide
with that of closure in the X topology of X*. Alaoglu [1; p. 256] and Kakutani [2; p.
170] independently established the equivalence of these types of closure without
...
124] also proved that in the case of a separable space these notions coincide
with that of closure in the X topology of X*. Alaoglu [1; p. 256] and Kakutani [2; p.
170] independently established the equivalence of these types of closure without
...
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Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
Copyright | |
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additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive Definition denote dense differential equations disjoint Doklady Akad Duke Math element ergodic theorem exists finite dimensional function defined Hausdorff space Hence Hilbert space homeomorphism ibid inequality integral Lebesgue Lebesgue measure Lemma linear functional linear map linear operator linear topological space measurable function 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 Sbornik N. S. scalar self-adjoint semi-group sequentially compact Show simple functions spectral Studia Math subset subspace Suppose theory topological space Trans uniformly Univ valued function Vber vector space weak topology weakly compact zero
Bibliographic information
| Title | Linear Operators: General theory Volume 7 of Pure and applied mathematics Volume 1 of Linear Operators, Jacob T. Schwartz Volume 7 of Pure and applied mathematics Interscience Press |
| Authors | Nelson Dunford, Jacob T. Schwartz |
| Publisher | Interscience Publishers, 1958 |
| Original from | the University of California |
| Digitized | 16 Mar 2011 |
| Length | 2592 pages |
| Subjects | › › Algebra, Universal Algebras, Linear Linear operators Mathematical analysis Mathematics / Algebra / Linear Mathematics / Mathematical Analysis |
| Export Citation | BiBTeX EndNote RefMan |