Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Averages of operators and their positivity

Author(s): Masaru Nagisa; Shuhei Wada
Journal: Proc. Amer. Math. Soc. 126 (1998), 499-506.
MSC (1991): Primary 47B65; Secondary 47B44
MathSciNet review: 1415335
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Abstract: Let $T$ be a bounded linear operator on a Hilbert space. We prove that $T$ is positive, if there exists a positive integer $N$ such that

$\begin{displaymath}\|I- {\frac{1 }{N+1 }}\sum \limits _{i=k}^{k+N} T^{i} \|, \|I- {\frac{1 }{N+2 }}\sum \limits _{i=k}^{k+N+1} T^{i} \| \le 1\end{displaymath}$

for any non-negative integer $k$ . For several commuting operators, we can extend this result and get the similar statement.

References:

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