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Fong, C. K.; Miers, C. R.; Sourour, A. R.

Lie and Jordan ideals of operators on Hilbert space. (English) Zbl 0509.47035

Proc. Am. Math. Soc. 84, 516-520 (1982).
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Cited in 4 Reviews
Cited in 18 Documents

MSC:

47L30 Abstract operator algebras on Hilbert spaces

Keywords:

operators on Hilbert spaces; Lie-ideal; Jordan ideals
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Full Text: DOI

References:

[1] Joel Anderson, Commutators of compact operators, J. Reine Angew. Math. 291 (1977), 128 – 132. · Zbl 0341.47025 · doi:10.1515/crll.1977.291.128
[2] Arlen Brown and Carl Pearcy, Compact restrictions of operators, Acta Sci. Math. (Szeged) 32 (1971), 271 – 282. · Zbl 0234.47019
[3] J. W. Calkin, Two-sided ideals and congruences in the ring of bounded operators in Hilbert space, Ann. of Math. (2) 42 (1941), 839 – 873. · Zbl 0063.00692 · doi:10.2307/1968771
[4] P. A. Fillmore, Sums of operators with square zero, Acta Sci. Math. (Szeged) 28 (1967), 285 – 288. · Zbl 0159.19302
[5] Paul R. Halmos, A Hilbert space problem book, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1967. · Zbl 0144.38704
[6] Paul R. Halmos and Shizuo Kakutani, Products of symmetries, Bull. Amer. Math. Soc. 64 (1958), 77 – 78. · Zbl 0084.10602
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[8] Carl Pearcy and David Topping, On commutators in ideals of compact operators, Michigan Math. J. 18 (1971), 247 – 252. · Zbl 0226.46066
[9] H. Radjavi, The group generated by involutions, Proc. Roy. Irish Acad. Sect. A 81 (1981), no. 1, 9 – 12. · Zbl 0431.47001
[10] Robert Schatten, Norm ideals of completely continuous operators, Ergebnisse der Mathematik und ihrer Grenzgebiete. N. F., Heft 27, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1960. · Zbl 0090.09402
[11] K. Shoda, Einige Sätze über Matrizen, Japan. J. Math. 13 (1936), 261-265.
[12] A. R. Sourour, A note on integral operators, Acta Sci. Math. (Szeged) 41 (1979), no. 3-4, 375 – 379. · Zbl 0437.47024
[13] Ian Stewart, The Lie algebra of endomorphisms of an infinite-dimensional vector space, Compositio Math. 25 (1972), 79 – 86. · Zbl 0241.17008
[14] David M. Topping, On linear combinations of special operators, J. Algebra 10 (1968), 516 – 521. · Zbl 0185.38801 · doi:10.1016/0021-8693(68)90077-X
[15] -, The unitarily invariant subspaces of \( \mathfrak{B}(\mathfrak{H})\), 1970, preprint.
[16] Gary Weiss, The Fuglede commutativity theorem modulo the Hilbert-Schmidt class and generating functions for matrix operators. II, J. Operator Theory 5 (1981), no. 1, 3 – 16. · Zbl 0478.47005
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