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A note on d-symmetric operators

Published online by Cambridge University Press:  17 April 2009

B. C. Gupta  and
P. B. Ramanujan
B. C. Gupta
Affiliation:
Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar 388120, Gujarat, India
P. B. Ramanujan
Affiliation:
Department of Mathematics, Saurashtra University, Rajkot 360 005, Gujarat, India.
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Abstract

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An operator T on a complex Hilbert space is d-symmetric if , where is the uniform closure of the range of the derivation operator δT(X)=TX−XT. It is shown that if the commutator ideal of the inclusion algebra for a d-symmetric operator is the ideal of all compact operators then T has countable spectrum and T is a quasidiagonal operator. It is also shown that if for a d-symmetric operator I(T) is the double commutant of T then T is diagonal.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 23 , Issue 3 , June 1981 , pp. 471 - 475
Copyright
Copyright © Australian Mathematical Society 1981

References

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