Decomposition of a Von Neumann Algebra Relative to a*-Automorphism
1979 ◽
Vol 22
(1)
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pp. 9-10
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Keyword(s):
Let X be any real or complex Banach space. If T is a bounded linear operator on X then denote by N(T) the null space of T and by R(T) the range space of T.Now if X is finite dimensional and N(T) = N(T2) then also R(T) = R(T2). Therefore X admits a direct sum decomposition.Indeed it is easy to see that N(T) = N(T2) implies that and, using dimension theory of finite dimensional spaces, that N(T) and R(T) span the whole space (see, for example, (2, pp. 271–73))
2001 ◽
Vol 27
(3)
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pp. 149-153
Keyword(s):
1979 ◽
Vol 31
(5)
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pp. 1012-1016
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Keyword(s):
1986 ◽
Vol 29
(1)
◽
pp. 15-21
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1997 ◽
Vol 56
(2)
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pp. 303-318
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Keyword(s):
1978 ◽
Vol 30
(5)
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pp. 1045-1069
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Keyword(s):
1984 ◽
Vol 96
(3)
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pp. 483-493
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1993 ◽
Vol 36
(2)
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pp. 197-209
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Keyword(s):
1981 ◽
Vol 22
(1)
◽
pp. 77-81
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1980 ◽
Vol 23
(2)
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pp. 227-230
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Keyword(s):