All the infinite nest algebras are isomorphic
Author:
Alvaro Arias
Journal:
Proc. Amer. Math. Soc. 115 (1992), 85-88
MSC:
Primary 47D25; Secondary 46L35
DOI:
https://doi.org/10.1090/S0002-9939-1992-1079694-1
MathSciNet review:
1079694
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: All the infinite nest algebras in a separable Hilbert space are completely isomorphic.
- [DGT] William J. Davis, D. J. H. Garling, and Nicole Tomczak-Jaegermann, The complex convexity of quasinormed linear spaces, J. Funct. Anal. 55 (1984), no. 1, 110–150. MR 733036, https://doi.org/10.1016/0022-1236(84)90021-1
- [L] David R. Larson, Nest algebras and similarity transformations, Ann. of Math. (2) 121 (1985), no. 3, 409–427. MR 794368, https://doi.org/10.2307/1971180
- [PPW] V. I. Paulsen, S. C. Power, and J. D. Ward, Semi-discreteness and dilation theory for nest algebras, J. Funct. Anal. 80 (1988), no. 1, 76–87. MR 960224, https://doi.org/10.1016/0022-1236(88)90066-3
- [Pe1] A. Pełczyński, Projections in certain Banach spaces, Studia Math. 19 (1960), 209–228. MR 0126145, https://doi.org/10.4064/sm-19-2-209-228
- [Pe2] Aleksander Pełczyński, Banach spaces of analytic functions and absolutely summing operators, American Mathematical Society, Providence, R.I., 1977. Expository lectures from the CBMS Regional Conference held at Kent State University, Kent, Ohio, July 11–16, 1976; Conference Board of the Mathematical Sciences Regional Conference Series in Mathematics, No. 30. MR 0511811
- [Po] Stephen Power, Analysis in nest algebras, Surveys of some recent results in operator theory, Vol. II, Pitman Res. Notes Math. Ser., vol. 192, Longman Sci. Tech., Harlow, 1988, pp. 189–234. MR 976846
- [R] J. R. Ringrose, On some algebras of operators. II, Proc. London Math. Soc. (3) 16 (1966), 385–402. MR 0196516, https://doi.org/10.1112/plms/s3-16.1.385
- [S] Andrzej Szankowski, 𝐵(\cal𝐻) does not have the approximation property, Acta Math. 147 (1981), no. 1-2, 89–108. MR 631090, https://doi.org/10.1007/BF02392870
- [W] P. Wojtaszczyk, On projections in spaces of bounded analytic functions with applications, Studia Math. 65 (1979), no. 2, 147–173. MR 557489, https://doi.org/10.4064/sm-65-2-147-173
does not have the approximation property, Acta Math. 147 (1981), 89-108. Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47D25, 46L35
Retrieve articles in all journals with MSC: 47D25, 46L35
Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1992-1079694-1
Keywords:
Nest algebra,
completely isomorphic
Article copyright:
© Copyright 1992
American Mathematical Society
