ASYMPTOTIC STABILITY I: COMPLETELY POSITIVE MAPS
2004 ◽
Vol 15
(03)
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pp. 289-312
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Keyword(s):
We show that for every "locally finite" unit-preserving completely positive map P acting on a C*, there is a corresponding *-automorphism α of another unital C*-algebra such that the two sequences P, P2, P3, … and α, α2, α3, … have the same asymptotic behavior. The automorphism α is uniquely determined by P up to conjugacy. Similar results hold for normal completely positive maps on von Neumann algebras, as well as for one-parameter semigroups. These results are operator algebraic counterparts of the classical theory of Perron and Frobenius on the structure of square matrices with nonnegative entries.
2014 ◽
Vol 26
(02)
◽
pp. 1450002
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1990 ◽
Vol 33
(4)
◽
pp. 434-441
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Keyword(s):
Keyword(s):
1997 ◽
Vol 55
(1)
◽
pp. 193-208
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Keyword(s):
2004 ◽
Vol 70
(1)
◽
pp. 101-116
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1978 ◽
Vol 21
(4)
◽
pp. 415-418
◽
2011 ◽
Vol 303
(2)
◽
pp. 555-594
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Keyword(s):
Keyword(s):
1981 ◽
Vol 33
(3)
◽
pp. 539-550
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Keyword(s):
1992 ◽
Vol 03
(02)
◽
pp. 185-204
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