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Transactions of the American Mathematical Society

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On the diagonal of an operator

Author: Peng Fan
Journal: Trans. Amer. Math. Soc. 283 (1984), 239-251
MSC: Primary 47A65; Secondary 47Bxx
MathSciNet review: 735419
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Abstract: Characterizations of zero-diagonal operators (i.e., operators that have a diagonal whose entries consist entirely of zeros) and the norm-closure of these operators are obtained. Also included are new characterizations of trace class operators, self-commutators of bounded operators, and others.

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  • [1] J. Anderson, Derivations, commutators and the essential numerical range, Ph.D. Thesis, Indiana University, 1971.
  • [2] A. Brown and C. Pearcy, Structure of commutators of operators, Ann. of Math. (2) 82 (1965), 112-127. MR 0178354 (31:2612)
  • [3] P. Fan and C. K. Fong, Which operators are the self-commutators of compact operators? Proc. Amer. Math. Soc. 80 (1980), 58-60. MR 574508 (81f:47024)
  • [4] P. Fillmore, On similarity and the diagonal of a matrix, Amer. Math. Monthly 76 (1969), 167-169. MR 0237526 (38:5807)
  • [5] P. Fillmore, C. K. Fong and A. Sourour, Real parts of quasinilpotent operators, Proc. Edinburgh Math. Soc. 22 (1979), 263-269. MR 560989 (81b:47021)
  • [6] P. Fillmore, J. Stampfli and J. Williams, On the essential numerical range, the essential spectrum and a problem of Halmos, Acta Sci. Math. (Szeged) 33 (1972), 179-192. MR 0322534 (48:896)
  • [7] P. R. Halmos, Finite-dimensional vector spaces, Van Nostrand, Princeton, N.J., 1958. MR 0089819 (19:725b)
  • [8] -, A Hilbert space problem book, Van Nostrand, Princeton, N.J., 1967. MR 0208368 (34:8178)
  • [9] H. Radjavi, Structure of $ {A^{\ast}}A - A{A^{\ast}}$, J. Math. Mech. 16 (1966), 19-26. MR 0203482 (34:3332)
  • [10] J. G. Stampfli and J. P. Williams, Growth conditions and the numerical range in a Banach algebra, Tôhoku Math. J. 20 (1968), 417-424. MR 0243352 (39:4674)
  • [11] Q. F. Stout, Schur products of operators and the essential numerical range, Trans. Amer. Math. Soc. 264 (1981), 39-47. MR 597865 (82h:47029)

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Keywords: Zero-diagonal operators, trace class operators, self-commutators
Article copyright: © Copyright 1984 American Mathematical Society

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