Maximal nests in the Calkin algebra

Author:
Don Hadwin

Journal:
Proc. Amer. Math. Soc. **126** (1998), 1109-1113

MSC (1991):
Primary 47D25, 04A30

DOI:
https://doi.org/10.1090/S0002-9939-98-04233-6

MathSciNet review:
1443829

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Abstract: We prove that if two countable commutative lattices of projections in the Calkin algebra are order isomorphic, then they are unitarily equivalent. We show that there are isomorphic maximal nests of projections in the Calkin algebra that are order isomorphic but not similar. Assuming the continuum hypothesis, we show that all maximal nests of projections in the Calkin algebra are order isomorphic.

**[A]**N. T. Andersen, Similarity of continuous nests, Bull. London Math. Soc. 15 (1983) 131-132. MR**85b:47049****[AD]**C. Apostol and K. R. Davidson, Isomorphisms modulo the compact operators of nest algebras, II, Duke Math. J. 6 (1988) no. 1, 101-127. MR**89g:47058****[AG]**C. Apostol and F. Gilfeather, Isomorphisms modulo the compact operators of nest algebras, Pacific J. Math. 122 (1986) 263-286. MR**87f:47063****[Ar]**W. B. Arveson, Perturbation theory for groups and lattices, J. Funct. Anal. 53 (1983) 22-73. MR**85d:47042****[BDF]**L. Brown, R. G. Douglas, and P. A. Fillmore, BDF**[CN]**W. W. Comfort and S. Negrepontis, The theory of ultrafilters, Springer-Verlag, Berlin, 1974. MR**53:135****[DW]**H. G. Dales and W. H. Woodin, An introduction to independence for analysts, London Math. Soc. Lecture Notes, No. 115, Cambridge Univ. Press, 1987. MR**90d:03101****[D1]**K. R. Davidson, Similarity and compact perturbations of nest algebras, J. Reine Angew. Math. 348 (1984), 286-294. MR**86c:47062****[D2]**K. Davidson, Nest algebras, Pitman Res. Notes Math. Ser., no. 191, Longman Sci. Tech., Harlow, 1988. MR**90f:47062****[H]**F. Hausdorff, Summen von Mengen, Fund. Math. 26 (1936) 241-255.**[JP]**B. E. Johnson and S. K. Parrott, Operators commuting with von Neumann algebras modulo the set of compact operators, J. Funct. Anal. 11 (1972) 39-61. MR**49:5869****[L]**D. R. Larson, A solution to a problem of J. R. Ringrose, Bull. Amer. Math. Soc. 7 (1982) 243-246. MR**83k:46046****[R]**C. A. Rickart, General theory of Banach algebras, Van Nostrand, Princeton, 1960. MR**22:5903****[vN1]**J. von Neumann, Charakterisierung des Spektrums eines Integral Operators, Hermann, Paris, 1935.

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Additional Information

**Don Hadwin**

Affiliation:
Department of Mathematics, University of New Hampshire, Durham, New Hampshire 03824

Email:
don@math.unh.edu

DOI:
https://doi.org/10.1090/S0002-9939-98-04233-6

Received by editor(s):
September 23, 1996

Communicated by:
Palle E. T. Jorgensen

Article copyright:
© Copyright 1998
American Mathematical Society