Linear Operators: General theory |
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Page 36
is commutative if the identity ab = ba is valid . A field is a commutative ring in
which the non - zero elements form a group under multiplication . The unit of this
group in a field will be written as 1 instead of e . A linear vector space , linear
space ...
is commutative if the identity ab = ba is valid . A field is a commutative ring in
which the non - zero elements form a group under multiplication . The unit of this
group in a field will be written as 1 instead of e . A linear vector space , linear
space ...
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and if T ( x + y ) = Tx + Ty , Tlax ) = a Tx for every a € 0 and every pair x , y of
vectors in the domain of T . Thus a linear transformation on a linear space X is a
homomorphism on the additive group X which commutes with the operations of ...
and if T ( x + y ) = Tx + Ty , Tlax ) = a Tx for every a € 0 and every pair x , y of
vectors in the domain of T . Thus a linear transformation on a linear space X is a
homomorphism on the additive group X which commutes with the operations of ...
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2 LEMMA . ( a ) In a topological group G , any algebraic combination of any
number of variables x1 , . . . 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
dy , .
2 LEMMA . ( a ) In a topological group G , any algebraic combination of any
number of variables x1 , . . . 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
dy , .
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Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
Copyright | |
31 other sections not shown
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Common terms and phrases
algebra Amer analytic applied arbitrary assumed B-space Banach spaces bounded called clear closed compact operator complex condition Consequently constant contains continuous functions converges convex convex set Corollary countably additive defined DEFINITION denote dense determined differential dimensional disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows formula function defined function f given Hence Hilbert space identity implies inequality integral interval Lebesgue Lemma limit linear functional linear operator linear space Math neighborhood norm operator operator topology problem projection PROOF properties proved range reflexive representation respect satisfies scalar seen semi-group separable sequence set function Show shown statement subset subspace sufficient Suppose Theorem theory topology u-measurable uniform uniformly unique unit sphere valued vector weak weakly compact zero
Bibliographic information
| Title | Linear Operators: General theory Part 1 of Linear Operators, Jacob T. Schwartz Volume 7 of Pure and applied mathematics Interscience Press Pure and applied mathematics Wiley classics library |
| Authors | Nelson Dunford, Jacob T. Schwartz |
| Publisher | Interscience Publishers, 1958 |
| Original from | the University of California |
| Digitized | 16 Mar 2011 |
| ISBN | 0470226056, 9780470226056 |
| Length | 2592 pages |
| Export Citation | BiBTeX EndNote RefMan |