The Furuta inequality in Banach *-algebras

Tanahashi, Kôtarô; Uchiyama, Atsushi

doi:10.1090/S0002-9939-99-05262-4

The Furuta inequality in Banach $*$-algebras
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by Kôtarô Tanahashi and Atsushi Uchiyama PDF

Proc. Amer. Math. Soc. 128 (2000), 1691-1695 Request permission

Abstract:

Let $0 < p, q, r \in \mathbb {R}$ be real numbers with $p+2r\leq (1+2r)q$ and $1\leq q.$ Furuta (1987) proved that if bounded linear operators $A, B \in B(H)$ on a Hilbert space $H$ satisfy $O\leq B \leq A$, then $B^{\frac {p+2r}{q}} \leq (B^{r}A^{p}B^{r})^{\frac {1}{q}}$. This inequality is called the Furuta inequality and has many applications. In this paper, we prove that the Furuta inequality holds in a unital hermitian Banach $*$-algebra with continuous involution.

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