Linear Operators: General theory |
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Page 289
PROOF . Let x * * € ( L * ) * . By Theorem 1 , L * is isometrically isomorphic to Lq ,
so that there is a functional y * e L * such that x * * ( * ) = y * ( g ) when g and x *
are connected , as in Theorem 1 , by the formula * * 1 = { s } ( s ) g ( s ) u ( ds ) , fel
...
PROOF . Let x * * € ( L * ) * . By Theorem 1 , L * is isometrically isomorphic to Lq ,
so that there is a functional y * e L * such that x * * ( * ) = y * ( g ) when g and x *
are connected , as in Theorem 1 , by the formula * * 1 = { s } ( s ) g ( s ) u ( ds ) , fel
...
Page 415
Hence ko e p - A , and thus pe A + k , CA + K . Q . E . D . Since the commutativity
of the group G is not essential to the proof , the same result holds for non -
Abelian topological groups . 4 LEMMA . For arbitrary sets A , B in a linear space X
: ( i ) ...
Hence ko e p - A , and thus pe A + k , CA + K . Q . E . D . Since the commutativity
of the group G is not essential to the proof , the same result holds for non -
Abelian topological groups . 4 LEMMA . For arbitrary sets A , B in a linear space X
: ( i ) ...
Page 434
and proceed as in the first part of the proof of the preceding theorem to construct
a subsequence { ym } of { { n } such that limm - * * * ym exists for each x * in the
set H of that proof . Let Rm = co { ym , Ym + 2 , . . . } and let yo be an arbitrary
point ...
and proceed as in the first part of the proof of the preceding theorem to construct
a subsequence { ym } of { { n } such that limm - * * * ym exists for each x * in the
set H of that proof . Let Rm = co { ym , Ym + 2 , . . . } and let yo be an arbitrary
point ...
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Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
Copyright | |
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