Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Algebraic isomorphisms and $\mathcal{J}$-subspace lattices


Authors: Jiankui Li and Oreste Panaia
Journal: Proc. Amer. Math. Soc. 133 (2005), 2577-2587
MSC (2000): Primary 47L10
Published electronically: April 15, 2005
MathSciNet review: 2146201
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The class of $\mathcal{J}$-lattices was originally defined in the second author's thesis and subsequently by Longstaff, Nation, and Panaia. A subspace lattice $\mathcal{L}$ on a Banach space $X$ which is also a $\mathcal{J}$-lattice is called a $\mathcal{J}$-subspace lattice, abbreviated JSL. It is demonstrated that every single element of $Alg\mathcal{L}$ has rank at most one. It is also shown that $Alg\mathcal{L}$has the strong finite rank decomposability property. Let $\mathcal{L}_1$ and $\mathcal{L}_2$ be subspace lattices that are also JSL's on the Banach spaces $X_1$ and $X_2$, respectively. The two properties just referred to, when combined, show that every algebraic isomorphism between $Alg\mathcal{L}_1$ and $Alg\mathcal{L}_2$ preserves rank. Finally we prove that every algebraic isomorphism between $Alg\mathcal{L}_1$ and $Alg\mathcal{L}_2$ is quasi-spatial.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 47L10

Retrieve articles in all journals with MSC (2000): 47L10


Additional Information

Jiankui Li
Affiliation: Department of Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
Email: jli@math.uwaterloo.ca

Oreste Panaia
Affiliation: School of Mathematics, The University of Western Australia, 35 Stirling Highway, Crawley, Western Australia 6009, Australia
Email: oreste@maths.uwa.edu.au

DOI: http://dx.doi.org/10.1090/S0002-9939-05-07581-7
PII: S 0002-9939(05)07581-7
Keywords: Algebraic isomorphism, rank-one operator, single element
Received by editor(s): February 4, 2002
Received by editor(s) in revised form: April 17, 2003
Published electronically: April 15, 2005
Communicated by: David R. Larson
Article copyright: © Copyright 2005 American Mathematical Society