Affiliation:
1. University of Niš, Department of Mathematics, Faculty of Electronic Engineering, Niš, Serbia
Abstract
In a recent paper, Curto et al. [4] asked the following question: ?Let T be a
subnormal operator, and assume that T2 is quasinormal. Does it follow that T
is quasinormal??. Pietrzycki and Stochel have answered this question in the
affirmative [18] and proved an even stronger result. Namely, the authors
have showed that the subnormal n-th roots of a quasinormal operator must be
quasinormal. In the present paper, using an elementary technique, we present
a much simpler proof of this result and generalize some other results from
[4]. We also show that we can relax a condition in the definition of
matricially quasinormal n-tuples and we give a correction for one of the
results from [4]. Finally, we give sufficient conditions for the equivalence
of matricial and spherical quasinormality of T(n,n) := (Tn 1, Tn 2 ) and
matricial and spherical quasinormality of T = (T1, T2), respectively.
Publisher
National Library of Serbia
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献