Linear Operators: General theory |
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Page 60
2\x\ ' £ ' This shows that (i) implies (iv). Statement (iv) clearly implies the continuity
of T at 0; so (iv) implies (ii). This (i), (ii), and (iv) are equivalent. If M = sup |Tai| is
finite, then for an arbitrary x =fc 0, This shows that (iii) implies (iv). It is obvious ...
2\x\ ' £ ' This shows that (i) implies (iv). Statement (iv) clearly implies the continuity
of T at 0; so (iv) implies (ii). This (i), (ii), and (iv) are equivalent. If M = sup |Tai| is
finite, then for an arbitrary x =fc 0, This shows that (iii) implies (iv). It is obvious ...
Page 280
That (1) implies (2) can be proved in a manner similar to that used in Theorem 14
to show that condition (3) of that theorem implies (4). From Corollary 19 it follows
that S may be embedded as a dense subset of a compact Hausdorff space St in ...
That (1) implies (2) can be proved in a manner similar to that used in Theorem 14
to show that condition (3) of that theorem implies (4). From Corollary 19 it follows
that S may be embedded as a dense subset of a compact Hausdorff space St in ...
Page 394
For example, a partially ordered vector space is a vector space SB in which there
is defined a relation x 22 y for some pairs of elements in SB for which (i) x 2; 0
and — x 2: 0 imply x — 0; (ii) x 2r y and y 2; z imply x 2; z; (iii) x 2: 0 and X a ...
For example, a partially ordered vector space is a vector space SB in which there
is defined a relation x 22 y for some pairs of elements in SB for which (i) x 2; 0
and — x 2: 0 imply x — 0; (ii) x 2r y and y 2; z imply x 2; z; (iii) x 2: 0 and X a ...
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Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries 84 | 34 |
Copyright | |
44 other sections not shown
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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 |
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