ACTA issues

## $\infty$-hyponormal operators and their spectral properties

Shizuo Miyajima, Isao Saito

Acta Sci. Math. (Szeged) 67:1-2(2001), 357-371
2788/2009

 Abstract. This article deals with operators that are $p$-hyponormal for every $p>0$ under the name of $\infty$-hyponormal operators. A characterization of such operators is given, and their properties are investigated. Special attention is paid to the spectral property of $\infty$-hyponormal operators having dense ranges and no non-trivial reducing subspaces. AMS Subject Classification (1991): 47B20, 47A63 Keyword(s): p, -hyponormal operator, spectral resolution, polar decomposition, spectrum, \infty, -hyponormal operator Received March 1, 2000, and in revised form September 12, 2000. (Registered under 2788/2009.)