Weighted n-shifts and M-hyponormality
type: Item
instance of: scholarly article
title: Weighted n-shifts and M-hyponormality
zbMATH Open document ID: 0581.47015
author: A. D. Thatte
author: A. D. Joshi
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 1985-01-01T00:00:00Z
review text: Weighted shifts are generalized by defining weighted n-shifts on a separable complex Hilbert space. The two main results of the paper provide a technique to produce a lot of examples of M-hyponormal weighted n-shifts with operator weights and with scalar weights. The only non- hyponormal M-hyponormal operator that was known previously was given by \textit{B. L. Wadhwa} [Duke Math. J. 41, 655-660 (1974; Zbl 0292.47021)] viz: weighted shift with weights 1,2,1,1,1... Also, hyponormal, quasi- hyponormal, paranormal weighted n-shifts and weighted n-shifts of class(M) are characterized. Examples are provided to show that the inclusion relations \[ (1)\quad hyponormal\quad \subseteq \quad M- hyponormal\quad \cap \quad quasi-hyponormal\quad \cap \quad class(M) \] and \[ (2)\quad class(N,k)\quad \cap \quad M-hyponormal\quad \subseteq \quad normaloid\quad \cap \quad M-hyponormal \] are proper.
Mathematics Subject Classification ID: 47B20
Mathematics Subject Classification ID: 47B37
zbMATH DE Number: 3929757
zbMATH Keywords: M-hyponormal weighted n-shifts with operator weights and with scalar weights
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3929757