Abstract
It is known that for (bounded) self-adjoint operators A,B on a Hilbert space H the infimum A ⋀ B, with respect to the order induced by the cone of positive (semi-definite) operators, exists only when A and B are comparable, that is, A ≥ B or A ≥ B. In this paper we present a necessary and sufficient condition for that, given A,B ≥ 0, the iniimum considered in the positive cone exists.
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© 1999 Springer Science+Business Media Dordrecht
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Ando, T. (1999). Problem of Infimum in the Positive Cone. In: Rassias, T.M., Srivastava, H.M. (eds) Analytic and Geometric Inequalities and Applications. Mathematics and Its Applications, vol 478. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4577-0_1
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DOI: https://doi.org/10.1007/978-94-011-4577-0_1
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