The Journal of the Indian Mathematical Society

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A Note on Generalized Commutators


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

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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.
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  • A Note on Generalized Commutators

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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.