Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On isomorphisms between certain non-CSL algebras

Author: Manos Papadakis
Journal: Proc. Amer. Math. Soc. 119 (1993), 1157-1164
MSC: Primary 47D25; Secondary 47A15
MathSciNet review: 1235101
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we characterize the existence of algebraic isomorphisms between certain reflexive algebras with two atom lattices. We also show by an example that these isomorphisms need not preserve certain geometric properties of their lattices.

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

  • [AKL] M. Anousis, A. Katavolos, and M. S. Lambrou, On the reflexive algebra with two invariant subspaces, J. Operator Theory (to appear). MR 1305508 (95i:47082)
  • [DH] K. Davidson and K. Harisson, Distance formulae for subspace lattices, J. London Math. Soc. 39 (1989), 309-323. MR 991664 (90g:47085)
  • [FW] P. A. Fillmore and J. P. Williams, On operator ranges, Adv. in Math. 7 (1971), 254-281. MR 0293441 (45:2518)
  • [GM] F. Gilfeather and R. Moore, Isomorphisms of Certain $ CSL$ algebras, J. Funct. Anal. 67 (1986), 264-291. MR 845200 (87k:47103)
  • [H] P. Halmos, Two subspaces, Trans. Amer. Math. Soc. 144 (1969), 381-389. MR 0251519 (40:4746)
  • [KLL] A. Katavolos, M. S. Lambrou, and W. E. Longstaff, The decomposability of operators relative to two subspaces, Studia Math. (to appear). MR 1222186 (94h:47082)
  • [KLP] A. Katavolos, M. S. Lambrou, and M. Papadakis, On some algebras diagonalised by $ M$-bases of $ {l^2}$, J. Integral Equations Operator Theory (to appear). MR 1220574 (95c:47048)
  • [L] M. S. Lambrou, Automatic continuity and implementation of homomorphisms, preprint.
  • [LAL] M. S. Lambrou and W. E. Longstaff, Spatiality of isomorphisms between certain reflexive algebras, preprint, 1993. MR 1216818 (95b:47053)
  • [LL] -, Unit ball density and the operator equation $ AX = BY$, J. Operator Theory 25 (1991), 383-397. MR 1203041 (94c:47026)
  • [P] M. Papadakis, On hyperreflexivity and rank one density for non-$ CSL$ algebras, Studia Math. 98 (1991). MR 1110095 (92g:47062)
  • [R] J. Ringrose, On some algebras of operators. II, Proc. London Math. Soc. 3 (1966), 385-402. MR 0196516 (33:4703)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47D25, 47A15

Retrieve articles in all journals with MSC: 47D25, 47A15

Additional Information

Keywords: Operator algebras, isomorphisms
Article copyright: © Copyright 1993 American Mathematical Society

American Mathematical Society