Quasi-P Normal operators linear operators on Hilbert space for which T+T* And T*T commute

AUTHOR AND
AFFILIATION

DIPSHIKHA BHATTACHARYA1 and NARENDRA PRASAD2
1,2Ramgarh College, Ramgarh Dept. of Mathematics Dist. Ramgarh Jharkhand, 829122 (V.B.U B Hazaribagh) (INDIA

KEYWORDS:

Quasi normal operator,Binormal operator,Hilbert Space

Issue Date:

August 2012

Pages:

ISSN:

2319-8044 (Online) – 2231-346X (Print)

Source:

Vol.24 – No.2

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DOI:

jusps-A

ABSTRACT:

Binormal operator: We say that an operator T on a Hilbert
Space H is bi-normal 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– P-normal operator : An operator T on a Hilbert Space
H is said to be quasi P-normal 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, “Quasi-P 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, “Quasi-P 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 bi-normal 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– P-normal operator : An operator T on a Hilbert Space
H is said to be quasi P-normal 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*