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Inequalities for the Schatten P-norm

Published online by Cambridge University Press:  18 May 2009

Fuad Kittaneh
Fuad Kittaneh
Affiliation:
Department of MathematicsUnited Arab Emirates Univ.P.O. Box 15551, Al-Ain, U.A.E.
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Let H be a separable, infinite dimensional complex Hilbert space, and let B(H) denote the algebra of all bounded linear operators on H. Let K(H) denote the ideal of compact operators on H. For any compact operator A let |A|=(A*A)1,2 and S1(A), s2(A),… be the eigenvalues of |A| in decreasing order and repeatedaccording to multiplicity. If, for some 1<p<∞, si(A)p <∞, we say that A is in the Schatten p-class Cp and ∥A∥p=1/p is the p-norm of A. Hence, C1 is the trace class, C2 is the Hilbert–Schmidt class, and C∞ is the ideal of compact operators K(H).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 26 , Issue 2 , July 1985 , pp. 141 - 143
Copyright
Copyright © Glasgow Mathematical Journal Trust 1985

References

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