The numerical index of nonselfadjoint operator algebras

Nakamura, Yoshihiro; Saito, Kichi-Suke; Sakaba, Kazunari

doi:10.1090/S0002-9939-1993-1118086-4

The numerical index of nonselfadjoint operator algebras
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by Yoshihiro Nakamura, Kichi-Suke Saito and Kazunari Sakaba PDF

Proc. Amer. Math. Soc. 117 (1993), 1105-1107 Request permission

Abstract:

Let $\mathfrak {A}$ be a (not necessarily selfadjoint) closed subalgebra of $B(H)$ that is the algebra of all bounded linear operators on a Hilbert space $H$. In this note, we prove that the range of numerical index of $\mathfrak {A}$ as an algebra is the whole of the interval $[\tfrac {1} {2},1]$.

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