Linear Operators: General theory |
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Page 50
2 Lemma, (a) In a topological group G, any algebraic combination of any number
of variables xv . . ., xn is continuous as a map of Gx. . . xG into G. (b) In a linear
topological space X, all linear combinations of any number of scalars *j, . . ., a^.
2 Lemma, (a) In a topological group G, any algebraic combination of any number
of variables xv . . ., xn is continuous as a map of Gx. . . xG into G. (b) In a linear
topological space X, all linear combinations of any number of scalars *j, . . ., a^.
Page 413
non-zero linear functional on the complex space X, which separates the sets M
and N. Q.E.D. 2. Linear Topological Spaces In this section, the results of Section
1 are applied to linear topological spaces. Statements 1—6 of this section are ...
non-zero linear functional on the complex space X, which separates the sets M
and N. Q.E.D. 2. Linear Topological Spaces In this section, the results of Section
1 are applied to linear topological spaces. Statements 1—6 of this section are ...
Page 419
T-closed subsets of X, /^-continuous maps, etc. will refer to the r topology of X.
The following lemma is a consequence of Definition 2. 3 Lemma. // jH is a total
linear space of linear junctionals on X, X is a locally convex linear topological
space ...
T-closed subsets of X, /^-continuous maps, etc. will refer to the r topology of X.
The following lemma is a consequence of Definition 2. 3 Lemma. // jH is a total
linear space of linear junctionals on X, X is a locally convex linear topological
space ...
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Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries 84 | 34 |
Copyright | |
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Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |
Common terms and phrases
Acad additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers contains continuous functions convex set Corollary countably additive Definition denote dense differential equations Doklady Akad Duke Math element equivalent exists finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral interval isometric isomorphism Lemma linear map linear operator linear topological space LP(S measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space null set open set operator topology positive measure space Proc properties proved real numbers reflexive Riesz Russian scalar semi-group sequentially compact Show simple functions subset subspace Suppose theory TM(S topological space Trans valued function Vber vector space weak topology weakly compact weakly sequentially compact zero
Bibliographic information
| Title | Linear Operators: General theory Volume 7 of Pure and applied mathematics Volume 1 of Linear Operators, Nelson Dunford |
| Authors | Nelson Dunford, Jacob T. Schwartz |
| Publisher | Interscience Publishers, 1958 |
| Original from | the University of Michigan |
| Digitized | 20 Nov 2007 |
| Length | 2592 pages |
| Subjects | › › Algebra, Universal Algebras, Linear Linear operators Mathematical analysis Mathematics / Algebra / Linear |
| Export Citation | BiBTeX EndNote RefMan |