Epigraph of operator functions |
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| Authors: | Mohsen Kian |
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| Institution: | 1. Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, P.O. Box 1339, Bojnord 94531, Iran;2. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395–5746, Tehran, Iran. |
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| Abstract: | It is known that a real function f is convex if and only if the set E(f) = {(x, y) ∈ ? × ?; f (x) ≤ y}, the epigraph of f is a convex set in ?2. We state an extension of this result for operator convex functions and C?-convex sets as well as operator log-convex functions and C?-log-convex sets. Moreover, the C?-convex hull of a Hermitian matrix has been represented in terms of its eigenvalues. |
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| Keywords: | 46L89 52A01 46L08 |
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