All the infinite nest algebras are isomorphic

Arias, Alvaro

doi:10.1090/S0002-9939-1992-1079694-1

All the infinite nest algebras are isomorphic
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Proc. Amer. Math. Soc. 115 (1992), 85-88 Request permission

Abstract:

All the infinite nest algebras in a separable Hilbert space are completely isomorphic.

References

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, DOI 10.1016/0022-1236(84)90021-1
David R. Larson, Nest algebras and similarity transformations, Ann. of Math. (2) 121 (1985), no. 3, 409–427. MR 794368, DOI 10.2307/1971180
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, DOI 10.1016/0022-1236(88)90066-3
A. Pełczyński, Projections in certain Banach spaces, Studia Math. 19 (1960), 209–228. MR 126145, DOI 10.4064/sm-19-2-209-228
Aleksander Pełczyński, Banach spaces of analytic functions and absolutely summing operators, Conference Board of the Mathematical Sciences Regional Conference Series in Mathematics, No. 30, 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. MR 0511811
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
J. R. Ringrose, On some algebras of operators. II, Proc. London Math. Soc. (3) 16 (1966), 385–402. MR 196516, DOI 10.1112/plms/s3-16.1.385
Andrzej Szankowski, $B({\cal H})$ does not have the approximation property, Acta Math. 147 (1981), no. 1-2, 89–108. MR 631090, DOI 10.1007/BF02392870
P. Wojtaszczyk, On projections in spaces of bounded analytic functions with applications, Studia Math. 65 (1979), no. 2, 147–173. MR 557489, DOI 10.4064/sm-65-2-147-173