AUTHOR AND 
DIPSHIKHA BHATTACHARYA1 and NARENDRA PRASAD2 
KEYWORDS: 
Quasi normal operator,Binormal operator,Hilbert Space 
Issue Date: 
August 2012 
Pages: 

ISSN: 
23198044 (Online) – 2231346X (Print) 
Source: 
Vol.24 – No.2 
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DOI: 
juspsA 
ABSTRACT:
Binormal operator: We say that an operator T on a Hilbert
Space H is binormal if TT* and T*T commute
i.e [T*T, TT*] = 0
I.e T*T TT* = TT*T*T = 0
Where T* is the ad joint of T
Quasi normal operator : We say that an operator T on a Hilbert
Space H is quasi normal operator if T and T*T commute
i.e [T , T*T] = 0
I.e TT*T = T*TT
Quasi– Pnormal operator : An operator T on a Hilbert Space
H is said to be quasi Pnormal operator if T+T* and T*T Commute
i.e [T+T* , T*T] = 0
I.e (T+T*) T*T = T*T(T+T*)
I.e TT*T+ T*T*T = T*TT+T*TT*
Copy the following to cite this Article:
DIPSHIKHA BHATTACHARYA1 and NARENDRA PRASAD2, “QuasiP Normal operators linear operators on Hilbert space for which T+T* And T*T commute”, Journal of Ultra Scientist of Physical Sciences, Volume 24, Issue 2, Page Number , 2016
Copy the following to cite this URL:
DIPSHIKHA BHATTACHARYA1 and NARENDRA PRASAD2, “QuasiP Normal operators linear operators on Hilbert space for which T+T* And T*T commute”, Journal of Ultra Scientist of Physical Sciences, Volume 24, Issue 2, Page Number , 2016
Available from: http://www.ultrascientist.org/paper/413/
Binormal operator: We say that an operator T on a Hilbert
Space H is binormal if TT* and T*T commute
i.e [T*T, TT*] = 0
I.e T*T TT* = TT*T*T = 0
Where T* is the ad joint of T
Quasi normal operator : We say that an operator T on a Hilbert
Space H is quasi normal operator if T and T*T commute
i.e [T , T*T] = 0
I.e TT*T = T*TT
Quasi– Pnormal operator : An operator T on a Hilbert Space
H is said to be quasi Pnormal operator if T+T* and T*T Commute
i.e [T+T* , T*T] = 0
I.e (T+T*) T*T = T*T(T+T*)
I.e TT*T+ T*T*T = T*TT+T*TT*