Weakly n-hyponormal Weighted Shifts and Their Examples |
| |
Authors: | George Exner Il Bong Jung Sang Soo Park |
| |
Institution: | (1) Department of Mathematics, Bucknell University, Lewisburg, Pennsylvania 17837, USA;(2) Department of Mathematics, Kyungpook National University, Taegu, 702-701, Korea |
| |
Abstract: | The gap between hyponormal and subnormal Hilbert space operators can be studied using the intermediate classes of weakly n-hyponormal and (strongly) n-hyponormal operators. The main examples for these various classes, particularly to distinguish them, have been the weighted
shifts. In this paper we first obtain a characterization for a weakly n-hyponormal weighted shift Wα with weight sequence α, from which we extend some known results for quadratically hyponormal (i.e., weakly 2-hyponormal)
weighted shifts to weakly n-hyponormal weighted shifts. In addition, we discuss some new examples for weakly n-hyponormal weighted shifts; one illustrates the differences among the classes of 2-hyponormal, quadratically hyponormal,
and positively quadratically hyponormal operators. |
| |
Keywords: | 47B37 47B20 |
本文献已被 SpringerLink 等数据库收录! |
|