Normal derivations in norm ideals

Kittaneh, Fuad

doi:10.1090/S0002-9939-1995-1242091-2

Normal derivations in norm ideals

Author: Fuad Kittaneh
Journal: Proc. Amer. Math. Soc. 123 (1995), 1779-1785
MSC: Primary 47B47; Secondary 47B10
DOI: https://doi.org/10.1090/S0002-9939-1995-1242091-2
MathSciNet review: 1242091
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: 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.

Joel Anderson, On normal derivations, Proc. Amer. Math. Soc. 38 (1973), 135–140. MR 312313, DOI https://doi.org/10.1090/S0002-9939-1973-0312313-6
Rajendra Bhatia and Fuad Kittaneh, Norm inequalities for partitioned operators and an application, Math. Ann. 287 (1990), no. 4, 719–726. MR 1066826, DOI https://doi.org/10.1007/BF01446925
Stephen L. Campbell and Ralph Gellar, Spectral properties of linear operators for which $T^ *T$ and $T$ $+$ $T^ *$ commute, Proc. Amer. Math. Soc. 60 (1976), 197–202 (1977). MR 417841, DOI https://doi.org/10.1090/S0002-9939-1976-0417841-3
B. P. Duggal, On generalised Putnam-Fuglede theorems, Monatsh. Math. 107 (1989), no. 4, 309–332. MR 1012463, DOI https://doi.org/10.1007/BF01517359
B. P. Duggal, A remark on normal derivations of Hilbert-Schmidt type, Monatsh. Math. 112 (1991), no. 4, 265–270. MR 1141094, DOI https://doi.org/10.1007/BF01351767
R. G. Douglas, On majorization, factorization, and range inclusion of operators on Hilbert space, Proc. Amer. Math. Soc. 17 (1966), 413–415. MR 203464, DOI https://doi.org/10.1090/S0002-9939-1966-0203464-1

S. N. Elalami, Opérateurs complètement finis, preprint.

Wen Ying Feng and Guo Xing Ji, A counterexample in the theory of derivations, Glasgow Math. J. 31 (1989), no. 2, 161–163. MR 997810, DOI https://doi.org/10.1017/S0017089500007679
I. C. Gohberg and M. G. Kreĭn, Introduction to the theory of linear nonselfadjoint operators, Translations of Mathematical Monographs, Vol. 18, American Mathematical Society, Providence, R.I., 1969. Translated from the Russian by A. Feinstein. MR 0246142
Paul Richard Halmos, A Hilbert space problem book, 2nd ed., Graduate Texts in Mathematics, vol. 19, Springer-Verlag, New York-Berlin, 1982. Encyclopedia of Mathematics and its Applications, 17. MR 675952
Fuad Kittaneh, On normal derivations of Hilbert-Schmidt type, Glasgow Math. J. 29 (1987), no. 2, 245–248. MR 901671, DOI https://doi.org/10.1017/S0017089500006893
P. J. Maher, Commutator approximants, Proc. Amer. Math. Soc. 115 (1992), no. 4, 995–1000. MR 1086335, DOI https://doi.org/10.1090/S0002-9939-1992-1086335-6
Robert Schatten, Norm ideals of completely continuous operators, Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Heft 27, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1960. MR 0119112
Barry Simon, Trace ideals and their applications, London Mathematical Society Lecture Note Series, vol. 35, Cambridge University Press, Cambridge-New York, 1979. MR 541149
Joseph G. Stampfli and Bhushan L. Wadhwa, An asymmetric Putnam-Fuglede theorem for dominant operators, Indiana Univ. Math. J. 25 (1976), no. 4, 359–365. MR 410448, DOI https://doi.org/10.1512/iumj.1976.25.25031
Katsutoshi Takahashi, On the converse of the Fuglede-Putnam theorem, Acta Sci. Math. (Szeged) 43 (1981), no. 1-2, 123–125. MR 621362
J. P. Williams, Finite operators, Proc. Amer. Math. Soc. 26 (1970), 129–136. MR 264445, DOI https://doi.org/10.1090/S0002-9939-1970-0264445-6
Takashi Yoshino, Subnormal operator with a cyclic vector, Tohoku Math. J. (2) 21 (1969), 47–55. MR 246145, DOI https://doi.org/10.2748/tmj/1178243033
Takashi Yoshino, Remark on the generalized Putnam-Fuglede theorem, Proc. Amer. Math. Soc. 95 (1985), no. 4, 571–572. MR 810165, DOI https://doi.org/10.1090/S0002-9939-1985-0810165-7