Abstract
We study approximation by commutators AX − XA, by generalized commutators AX − XB and by self–commutators X ∗ X − XX ∗ for varying X in the context of \(\mathcal{L}(H)\) and \(\mathcal{C}_{p}\).
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J.G. Aiken, J.A. Erdos, J.A. Goldstein, Unitary approximation of positive operators. Ill. J. Math. 24, 61–72 (1980)
N.I. Akheiser, I.M. Glazman, in Theory of Linear Operators in Hilbert Space, vol. II (Unger, New York, 1963)
J. Anderson, On normal derivations. Proc. Am. Math. Soc. 38, 135–140 (1973)
J. Anderson, C. Foias, Properties which normal operators share with derivations and related operators. Pac. J. Math. 61, 313–325 (1975)
S. Bouali, S. Cherki, Approximation by generalized commutators. Acta Sci. Math. (Szeged) 63, 272–278 (1997)
H. Dunford, J.T. Schwartz, Linear Operators, Part II (Interscience, New York, 1963)
J.A. Erdos, On the trace of a trace class operator. Bull. Lond. Math. Soc. 6, 47–50 (1974)
P.R. Halmos, Commutators of operators, II. Am. J. Math. 76, 191–198 (1954)
P.R. Halmos, A Hilbert Space Problem Book, 2nd edn. (Springer, New York, 1974)
D.C. Kleinecke, On operator commutators. Proc. Am. Math. Soc. 8, 535–536 (1957)
P.J. Maher, Commutator approximants. Proc. Am. Math. Soc. 115, 995–1000 (1992)
P.J. Maher, Self-commutator approximants. Proc. Am. Math. Soc. 134, 157–165 (2007)
P.J. Maher, Commutator and self-commutator approximants, II. Filomat 24(4), 1–7 (2010). www.pmf.ni.ac,yu/sajt/publiRacije/publiKacije–pocetna
E.W. Packel, Functional Analysis: A Short Course (Intertext, New York, 1974)
J.R. Ringrose, Compact Non-Self-Adjoint Operators (Van Nostrand Rheinhold, London, 1971)
P.V. Shirokov, Proof of a conjecture of Kaplansky. Usp. Mat. Nauk 11, 161–168 (1956)
H. Wielandt, Ueber die Unbeschränktheit der Operatoren des Quantenmechanik. Math. Ann. 121, 21 (1949)
A. Wintner, The unboundedness of quantum-mechanical matrices. Phys. Rev. 71, 738–739 (1947)
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Maher, P.J. (2017). Commutator Approximants. In: Operator Approximant Problems Arising from Quantum Theory. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-61170-9_4
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DOI: https://doi.org/10.1007/978-3-319-61170-9_4
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Publisher Name: Birkhäuser, Cham
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