کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4624016 | 1339529 | 2006 | 14 صفحه PDF | دانلود رایگان |
This paper considers the k-hyperexpansive Hilbert space operators T (those satisfying , 1⩽n⩽k) and the k-expansive operators (those satisfying the above inequality merely for n=k). It is known that if T is k-hyperexpansive then so is any power of T; we prove the analogous result for T assumed merely k-expansive. Turning to weighted shift operators, we give a characterization of k-expansive weighted shifts, and produce examples showing the k-expansive classes are distinct. For a weighted shift W that is k-expansive for all k (that is, completely hyperexpansive) we obtain results for k-hyperexpansivity of back step extensions of W. In addition, we discuss the completely hyperexpansive completion problem which is parallel to Stampfli's subnormal completion problem.
Journal: Journal of Mathematical Analysis and Applications - Volume 323, Issue 1, 1 November 2006, Pages 569-582