TY - JOUR

T1 - Operator maps of Jensen-type

AU - Hansen, Frank

AU - Moslehian, Mohammad Sal

AU - Najafi, Hamed

N1 - Funding Information:
The third author was supported by a grant from Ferdowsi University of Mashhad
Funding Information:
The third author was supported by a grant from Ferdowsi University of Mashhad (No. 2/46186).

PY - 2018/11/1

Y1 - 2018/11/1

N2 - Let BJ(H) denote the set of self-adjoint operators acting on a Hilbert space H with spectra contained in an open interval J. A map Φ : BJ(H) → B(H) sa is said to be of Jensen-type if Φ(C∗AC+D∗BD)≤C∗Φ(A)C+D∗Φ(B)Dfor all A, B∈ BJ(H) and bounded linear operators C, D acting on H with C∗C+ D∗D= I, where I denotes the identity operator. We show that a Jensen-type map on an infinite dimensional Hilbert space is of the form Φ (A) = f(A) for some operator convex function f defined in J.

AB - Let BJ(H) denote the set of self-adjoint operators acting on a Hilbert space H with spectra contained in an open interval J. A map Φ : BJ(H) → B(H) sa is said to be of Jensen-type if Φ(C∗AC+D∗BD)≤C∗Φ(A)C+D∗Φ(B)Dfor all A, B∈ BJ(H) and bounded linear operators C, D acting on H with C∗C+ D∗D= I, where I denotes the identity operator. We show that a Jensen-type map on an infinite dimensional Hilbert space is of the form Φ (A) = f(A) for some operator convex function f defined in J.

KW - Convex operator function

KW - Jensen’s operator inequality

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U2 - 10.1007/s11117-018-0571-8

DO - 10.1007/s11117-018-0571-8

M3 - Article

AN - SCOPUS:85042907083

VL - 22

SP - 1255

EP - 1263

JO - Positivity

JF - Positivity

SN - 1385-1292

IS - 5

ER -