Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 8 (2013), 23 -- 34

POSITIVE BLOCK MATRICES ON HILBERT AND KREIN C*-MODULES

M. Dehghani, S. M. S. Modarres and M. S. Moslehian

Abstract. Let H1 and H2 be Hilbert C*-modules. In this paper we give some necessary and sufficient conditions for the positivity of a block matrix on the Hilbert C*-module H1⊕H2.

2010 Mathematics Subject Classification: Primary 47B50; Secondary 46L08; 46C20; 47B65.
Keywords: Block matrix; Indefinite inner product module; J-positive operator; J-contraction; Krein C*-module.

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Mohammad Sal Moslehian Mahdi Dehghani
Department of Pure Mathematics, Department of Pure and Applied Mathematics,
Center of Excellence in Analysis on Yazd University,
Algebraic Structures (CEAAS), Yazd P.O. Box 89195-741, Iran.
Ferdowsi University of Mashhad, Department of Pure Mathematics,
P. O. Box 1159, Mashhad 91775, Iran. Center of Excellence in Analysis on
e-mail: moslehian@um.ac.ir, Algebraic Structures (CEAAS),
moslehian@member.ams.org Ferdowsi University of Mashhad,
P. O. Box 1159, Mashhad 91775, Iran.
e-mail: e.g.mahdi@gmail.com
Seyed Mohammad Sadegh Modarres
Department of Pure and Applied Mathematics,
Yazd University,
Yazd P. O. Box 89195-741, Iran.
e-mail: smodares@yazduni.ac.ir

http://www.utgjiu.ro/math/sma