The Journal of the Indian Mathematical Society

Open Access Open Access  Restricted Access Subscription Access
Open Access Open Access Open Access  Restricted Access Restricted Access Subscription Access

A Note on Generalized Commutators


Affiliations
1 Department of Mathematics, University of Delhi, Delhi-110007, India
     

   Subscribe/Renew Journal


An Operator T on a Hilbert space H is said to be positive semidefinite (negative semi definite) if (Tx, x) ≥ 0 ((Tx, x) ≤ 0 ) ∀ x ∈ H . T is said to be semidefinite if it is either positive semidefinite or negative semidefinite. If (Tx, x) > 0((Tx, x) < 0) ∀ x ∈ H, then T is called positive definite (negative definite). T is defined to be definite if it is either positive definite or negative definite.
Subscription Login to verify subscription
User
Notifications
Font Size


Abstract Views: 144

PDF Views: 0




  • A Note on Generalized Commutators

Abstract Views: 144  |  PDF Views: 0

Authors

Subhash Chander
Department of Mathematics, University of Delhi, Delhi-110007, India
Lovnta Mangla
Department of Mathematics, University of Delhi, Delhi-110007, India

Abstract


An Operator T on a Hilbert space H is said to be positive semidefinite (negative semi definite) if (Tx, x) ≥ 0 ((Tx, x) ≤ 0 ) ∀ x ∈ H . T is said to be semidefinite if it is either positive semidefinite or negative semidefinite. If (Tx, x) > 0((Tx, x) < 0) ∀ x ∈ H, then T is called positive definite (negative definite). T is defined to be definite if it is either positive definite or negative definite.