Geodesic
THE LÖWNER-HEINZINEQUALITY IN BANACH *-ALGEBRAS
Glasgow mathematical journal, Tome 42 (2000) no. 2, pp. 243-246

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We prove the Löwner-Heinz inequality, via the Cordesinequality, for elements a,b>0 of a unital hermitian Banach *-algebra A.Letting p be a real number in the interval (0,1], the former asserts that a^p \leb^p if a \le b, a^p < b^p ifa<b, provided that the involution of A is continuous, and the latterthat s(a^pb^p) \le s(ab)^p, where s(x)=r(x^*x)^{1/2} andr(x) is the spectral radius of an elementx. 
THE LÖWNER-HEINZINEQUALITY IN BANACH *-ALGEBRAS. Glasgow mathematical journal, Tome 42 (2000) no. 2, pp. 243-246. doi: 10.1017/S0017089500020097
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