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Linear preservers of isomorphic types of lattices of invariant operator ranges

Author(s): Leiba Rodman; Nahum Zobin
Journal: Proc. Amer. Math. Soc. 129 (2001), 2981-2986.
MSC (2000): Primary 47A15, 47B49
Posted: February 15, 2001
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Abstract: We describe all linear self-mappings of the space of bounded linear operators in an infinite dimensional separable complex Hilbert space which preserve the isomorphism class of the lattice of invariant operator ranges.

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Additional Information:

Leiba Rodman
Affiliation: Department of Mathematics, College of William and Mary, P.O. Box 8795, Williamsburg, Virginia 23187-8795
Email: lxrodm@math.wm.edu

Nahum Zobin
Affiliation: Department of Mathematics, College of William and Mary, P.O. Box 8795, Williamsburg, Virginia 23187-8795
Email: zobin@math.wm.edu

DOI: 10.1090/S0002-9939-01-05973-1
PII: S 0002-9939(01)05973-1
Keywords: Invariant operator ranges, linear preservers
Received by editor(s): February 23, 2000
Posted: February 15, 2001
Additional Notes: The research of the first author was partially supported by NSF Grant DMS-9800704
Communicated by: Joseph A. Ball
Copyright of article: Copyright 2001, American Mathematical Society

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