Normal derivations in norm ideals. (English) Zbl 0831.47036

Kittaneh, Fuad

Proc. Am. Math. Soc. 123, No. 6, 1779-1785 (1995).

Summary: We establish the orthogonality of the range and the kernel of a normal derivation with respect to the unitarily invariant norms associated with norm ideals of operators. Related orthogonality results for certain nonnormal derivations are also given.

MSC:

47L20	Operator ideals
47B10	Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.)
47B47	Commutators, derivations, elementary operators, etc.
47A30	Norms (inequalities, more than one norm, etc.) of linear operators
47B15	Hermitian and normal operators (spectral measures, functional calculus, etc.)
47B20	Subnormal operators, hyponormal operators, etc.
46B20	Geometry and structure of normed linear spaces

Keywords:

orthogonality of the range and the kernel of a normal derivation; unitarily invariant norms associated with norm ideals of operators; nonnormal derivations

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