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On \((n,k)\)-Quasi-\(*\)-paranormal Operators

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Abstract

For nonnegative integers \(n\) and \(k\), we introduce in this paper a new class of \((n,k)\)-quasi-\(*\)-paranormal operators satisfying

$$\begin{aligned} ||T^{1+n}(T^{k}x)||^{1/(1+n)}||T^{k}x||^{n/(1+n)} \ge ||T^*(T^{k}x)|| \text { for all } x \in H. \end{aligned}$$

This class includes the class of \(n\)-\(*\)-paranormal operators and the class of \((1,k)\)-quasi-\(*\)-paranormal operators contains the class of \(k\)-quasi-\(*\)-class \(A\) operators. We study the basic properties of \((n,k)\)-quasi-\(*\)-paranormal operators, like relations of this new class of operators with other classes known in the literature, their matrix representation, and properties of their spectra.

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Acknowledgments

The authors express their sincere thanks to Professor Jiangtao Yuan for sending us the papers [24, 25, 27]. This work has been supported by National Natural Science Foundation of China (11401097, 11171066, 11201071, 11301077, 11301078).

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Authors and Affiliations

  1. College of Computer and Information Sciences, Fujian Agriculture and Forestry University, Fuzhou, 350002, People’s Republic of China

    Qingping Zeng

  2. School of Mathematics and Computer Science, Fujian Normal University, Fuzhou, 350007, People’s Republic of China

    Huaijie Zhong

Authors
  1. Qingping Zeng
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  2. Huaijie Zhong
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Correspondence to Qingping Zeng.

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Communicated by Mohammad Sal Moslehian.

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Zeng, Q., Zhong, H. On \((n,k)\)-Quasi-\(*\)-paranormal Operators. Bull. Malays. Math. Sci. Soc. 40, 1363–1376 (2017). https://doi.org/10.1007/s40840-015-0119-z

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  • DOI: https://doi.org/10.1007/s40840-015-0119-z

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