On the convexity of functions
Keyword(s):
Let A,B, and X be bounded linear operators on a separable Hilbert space such that A,B are positive, X ? ?I, for some positive real number ?, and ? ? [0,1]. Among other results, it is shown that if f(t) is an increasing function on [0,?) with f(0) = 0 such that f(?t) is convex, then ?|||f(?A + (1-?)B) + f(?|A-B|)|||?|||?f(A)X + (1-?)Xf (B)||| for every unitarily invariant norm, where ? = min (?,1-?). Applications of our results are given.
1974 ◽
Vol 26
(3)
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pp. 565-575
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Keyword(s):
1971 ◽
Vol 23
(1)
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pp. 132-150
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1981 ◽
Vol 33
(6)
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pp. 1291-1308
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2020 ◽
Vol 18
(05)
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pp. 2050033
Keyword(s):
1982 ◽
Vol 33
(1)
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pp. 135-142
1999 ◽
Vol 42
(1)
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pp. 87-96
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1986 ◽
Vol 29
(2)
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pp. 255-261
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2005 ◽
Vol 2005
(20)
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pp. 3237-3245
2004 ◽
Vol 56
(4)
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pp. 742-775
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