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On normal derivations of Hilbert–Schmidt type

Published online by Cambridge University Press:  18 May 2009

Fuad Kittaneh
Fuad Kittaneh*
Affiliation:
Department of Mathematics, United Arab Emirates University, P.O. Box 15551, Al-Ain, U.A.E.
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Let H denote a separable, infinite dimensional Hilbert space. Let B(H), C2 and C1 denote the algebra of all bounded linear operators acting on H, the Hilbert–Schmidt class and the trace class in B(H) respectively. It is well known that C2 and C1 each form a two-sided-ideal in B(H) and C2 is itself a Hilbert space with the inner product

where {ei} is any orthonormal basis of H and tr(.) is the natural trace on C1. The Hilbert–Schmidt norm of X ∈ C2 is given by ⅡXⅡ2=(X, X)½.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 29 , Issue 2 , July 1987 , pp. 245 - 248
Copyright
Copyright © Glasgow Mathematical Journal Trust 1987

References

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