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Elementary operators on 𝒥-subspace lattice algebras

Published online by Cambridge University Press:  17 April 2009

Pengtong Li  and
Fangyan Lu
Pengtong Li
Affiliation:
Department of Mathematics, College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, People's Republic of China, e-mail: [email protected]
Fangyan Lu
Affiliation:
Department of Mathematics, Suzhou University, Suzhou 215006, People's Republic of China, e-mail: [email protected]
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Abstract

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The abstract concept of an elementary operator was recently introduced and studied by other authors. In this paper, we describe the general form of elementary operators between standard subalgebras of 𝒥-subspace lattice algebras. The result can apply to atomic Boolean subspace lattice algebras and pentagon subspace lattice algebras.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 68 , Issue 3 , December 2003 , pp. 395 - 404
Copyright
Copyright © Australian Mathematical Society 2003

References

[1]Brešar, M. and Šemrl, P., ‘Elementary operators’, Proc. Roy. Soc. Edinburgh, Sect. A 129 (1999), 1115–1135.CrossRefGoogle Scholar
[2]Brešar, M., Molnár, L. and Šemrl, P., ‘Elementary operators II’, Acta Sci. Math. (Szeged) 66 (2000), 769–791.Google Scholar
[3]Johnson, B.E., ‘An introduction to the theory of centralizers’, Proc. London Math. Soc. 14 (1964), 299–320.CrossRefGoogle Scholar
[4]Katavolos, A., Lambrou, M.S. and Longstaff, W.E., ‘Pentagon subspace lattices on Banach spaces’, J. Operator Theory 46 (2001), 355–380.Google Scholar
[5]Lambrou, M.S., ‘On the rank of operators in reflexive algebras’, Linear Algebra Appl. 142 (1990), 211–235.CrossRefGoogle Scholar
[6]Lambrou, M.S. and Longstaff, W.E., ‘Non-reflexive pentagon subspace lattices’, Studia Math. 125 (1997), 187–199.CrossRefGoogle Scholar
[7]Li, P. and Ma, J., ‘Derivations, local derivations and atomic Boolean subspace lattices’, Bull. Austral. Math. Soc. 66 (2002), 477–486.CrossRefGoogle Scholar
[8]Longstaff, W.E., ‘Strongly reflexive lattices’, J. London Math. Soc. 11 (1975), 491–498.CrossRefGoogle Scholar
[9]Longstaff, W.E., Nation, J.B. and Panaia, O., ‘Abstract reflexive sublattices and completely distributive collapsibility’, Bull. Austral. Math. Soc. 58 (1998), 245–260.CrossRefGoogle Scholar
[10]Longstaff, W.E. and Panaia, O., ‘,–subspace lattices and subspace M–bases’, Studia Math. 139 (2000), 197–211.Google Scholar
[11]Lu, F. and Li, P., ‘Algebraic isomorphisms and Jordan derivations of -subspace lattice algebras’, Studia Math. 158 (2003), 287–301.CrossRefGoogle Scholar
[12]Lu, F. and Li, P., ‘Jordan isomorphisms of -subspace lattice algebras’, Linear Algebra Appl. 371 (2003), 255–264.CrossRefGoogle Scholar
[13]Molnár, L. and Šemrl, P., ‘Elementary operators on standard operator algebras’, Linear and Multilinear Algebra 50 (2002), 315–319.CrossRefGoogle Scholar
[14]Panaia, O., Quasi–spatiality of isomorphisms for certain classes of operator algebras, Ph.D. Dissertation (University of Western Australia, Australia, 1995).Google Scholar