## Annals of Functional Analysis

### $p$-Quasiposinormal Composition and Weighted Composition Operators on $L^2(\mu)$

#### Abstract

An operator $T$ on a Hilbert space $H$ is called $p$-quasiposinormal operator if $c^2T^*(T^*T)^pT\ge T^*(TT^*)^pT$ where $p \in (0, 1]$ and for some $c\in (0, \infty)$. In this paper, we have obtained conditions for composition and weighted composition operators to be $p$-quasiposinormal operators.

#### Article information

Source
Ann. Funct. Anal., Volume 6, Number 1 (2015), 109-115.

Dates
First available in Project Euclid: 19 December 2014

https://projecteuclid.org/euclid.afa/1419001454

Digital Object Identifier
doi:10.15352/afa/06-1-9

Mathematical Reviews number (MathSciNet)
MR3297791

Zentralblatt MATH identifier
1312.47030

Subjects
Primary: 47B38
Secondary: 47B20: Subnormal operators, hyponormal operators, etc. 47B33: Composition operators

#### Citation

Gupta, Anuradha; Bhatia, Neha. $p$-Quasiposinormal Composition and Weighted Composition Operators on $L^2(\mu)$. Ann. Funct. Anal. 6 (2015), no. 1, 109--115. doi:10.15352/afa/06-1-9. https://projecteuclid.org/euclid.afa/1419001454

#### References

• G. Datt, On k-Quasiposinormal Weighted composition operators, Thai J. Math. 11 (2013), no. 1, 131–142.
• D.J. Harrington and R. Whitley, Seminormal composition operator, J. Operator Theory 11 (1984), 125–135.
• M.R. Jabbarzadeh and M.R. Azimi, Some weak hyponormal classes of weighted composition operators, Bull. Korean Math. Soc. 47 (2010), no. 4, 793–803.
• B.S. Komal and S. Gupta, Composition operators on Orlicz space, Indian J. Pure Appl. Math. 32 (2001), no. 7, 1117–1122.
• B.S. Komal, V. Khosla and K. Raj, On operators of weighted composition on Orlicz sequence spaces, Int. J. Contemp. Math. Sci. 5 (2010), no. 40, 1961–1968.
• M.Y. Lee and S.H. Lee, On $(p,k)$-quasiposinormal operators, J. Appl. Math Comput. 19 (2005), no. 1-2, 573–578.
• R.K. Singh, Compact and quasinormal composition operators, Proc. Amer. Math. Soc. 45 (1974), 80–82.