caa a22 4500 386372349 CHVBK 20180307112002.0 cr unu---uuuuu 161130e198905 xx s 000 0 eng 10.1017/S0017089500007679 doi S0017089500007679 pii (NATIONALLICENCE)cambridge-10.1017/S0017089500007679 A Counterexample in the theory of derivations [Elektronische Daten] Let B(H) be the algebra of all bounded linear operators on a separable, infinite dimensional complex Hilbert space H. Let C2 and C1 denote respectively, the Hilbert-Schmidt class and the trace class operators in B(H). It is known that C2 and C1 are two-sided*-ideals in B(H) and C2 is a Hilbert space with respect to the inner product (where tr denotes the trace). For any Hilbert-Schmidt operator X let X2=(X, X)½ be the Hilbert-Schmidt norm of X. For fixed A B(H) let δA be the operator on B(H) defined by Operators of the form (1) are called inner derivations and they (as well as their restrictions have been extensively studied (for example [1-3]). In [1], Fuad Kittaneh proved the following result. Copyright © Glasgow Mathematical Journal Trust 1989 Wenying Feng Department of Mathematics, Shaanxi Normal University, Xi'an, People's Republic of China Guoxing Ji Department of Mathematics, Shaanxi Normal University, Xi'an, People's Republic of China Glasgow Mathematical Journal Cambridge University Press 31/2(1989-05), 161-163 0017-0895 31:2<161 1989 31 GMJ https://doi.org/10.1017/S0017089500007679 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0017089500007679 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Wenying Feng Department of Mathematics, Shaanxi Normal University, Xi'an, People's Republic of China NATIONALLICENCE 700 1- Guoxing Ji Department of Mathematics, Shaanxi Normal University, Xi'an, People's Republic of China NATIONALLICENCE 773 0- Glasgow Mathematical Journal Cambridge University Press 31/2(1989-05), 161-163 0017-0895 31:2<161 1989 31 GMJ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge