A Note on Generalized Commutators

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Authors

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

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.

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Published

1974-12-01

How to Cite

Chander, S., & Mangla, L. (1974). A Note on Generalized Commutators. The Journal of the Indian Mathematical Society, 38(1-4), 355–357. Retrieved from https://informaticsjournals.co.in/index.php/jims/article/view/16711

Issue

Volume 38, Issue 1-4, March-December 1974

Section

Articles

License

Copyright (c) 1974 Subhash Chander, Lovnta Mangla

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

 

References

G. EDGAR, J. ERNEST AND S. G. LEE, Weighing operator spectra, Indiana University Mathematical Journal 21 (1971) 61-80.

P. R. HALMOS, A Hilbert space problem book, D. van Nostrand Co. Inc., 1967.

C. R. PUTNAM, On commutators of bounded matrices, Amer. J. Math. 73 (1951) 127-131.