Generalizations of certain nest algebra results
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- by N. K. Spanoudakis PDF
- Proc. Amer. Math. Soc. 115 (1992), 711-723 Request permission
Abstract:
In this paper we discuss generalizations from the Hilbert space case to more general settings of certain theorems concerning a nest algebra $\mathcal {L}$, namely, (a) the solvability of $Tx = y$ within $\operatorname {Alg} \mathcal {L}$, (b) the decomposability of finite rank operators of $\operatorname {Alg} \mathcal {L}$ by rank one such operators, and (c) approximability in the strong operator topology of $\operatorname {Alg} \mathcal {L}$ by its finite ranks.References
- G. D. Allen, D. R. Larson, J. D. Ward, and G. Woodward, Similarity of nests in $\textbf {L}_1$, J. Funct. Anal. 92 (1990), no. 1, 49–76. MR 1064686, DOI 10.1016/0022-1236(90)90067-U
- S. Argyros, M. Lambrou, and W. E. Longstaff, Atomic Boolean subspace lattices and applications to the theory of bases, Mem. Amer. Math. Soc. 91 (1991), no. 445, iv+94. MR 1052372, DOI 10.1090/memo/0445
- J. A. Erdos, Unitary invariants for nests, Pacific J. Math. 23 (1967), 229–256. MR 222702
- J. A. Erdos, Operators of finite rank in nest algebras, J. London Math. Soc. 43 (1968), 391–397. MR 230156, DOI 10.1112/jlms/s1-43.1.391
- K. J. Harrison and W. E. Longstaff, Automorphic images of commutative subspace lattices, Trans. Amer. Math. Soc. 296 (1986), no. 1, 217–228. MR 837808, DOI 10.1090/S0002-9947-1986-0837808-1
- Alan Hopenwasser, Cecelia Laurie, and Robert Moore, Reflexive algebras with completely distributive subspace lattices, J. Operator Theory 11 (1984), no. 1, 91–108. MR 739795
- Alan Hopenwasser and Robert Moore, Finite rank operators in reflexive operator algebras, J. London Math. Soc. (2) 27 (1983), no. 2, 331–338. MR 692538, DOI 10.1112/jlms/s2-27.2.331
- M. S. Lambrou, Approximants, commutants and double commutants in normed algebras, J. London Math. Soc. (2) 25 (1982), no. 3, 499–512. MR 657507, DOI 10.1112/jlms/s2-25.3.499
- M. S. Lambrou and W. E. Longstaff, Unit ball density and the operator equation $AX=YB$, J. Operator Theory 25 (1991), no. 2, 383–397. MR 1203041
- E. C. Lance, Some properties of nest algebras, Proc. London Math. Soc. (3) 19 (1969), 45–68. MR 241990, DOI 10.1112/plms/s3-19.1.45
- David R. Larson, On similarity of nests in Hilbert space and in Banach spaces, Functional analysis (Austin, TX, 1986–87) Lecture Notes in Math., vol. 1332, Springer, Berlin, 1988, pp. 179–194. MR 967097, DOI 10.1007/BFb0081620
- David R. Larson and Warren R. Wogen, Reflexivity properties of $T\oplus 0$, J. Funct. Anal. 92 (1990), no. 2, 448–467. MR 1069253, DOI 10.1016/0022-1236(90)90058-S
- Cecelia Laurie and W. E. Longstaff, A note on rank-one operators in reflexive algebras, Proc. Amer. Math. Soc. 89 (1983), no. 2, 293–297. MR 712641, DOI 10.1090/S0002-9939-1983-0712641-2
- W. E. Longstaff, Operators of rank one in reflexive algebras, Canadian J. Math. 28 (1976), no. 1, 19–23. MR 397435, DOI 10.4153/CJM-1976-003-1
- J. R. Ringrose, On some algebras of operators, Proc. London Math. Soc. (3) 15 (1965), 61–83. MR 171174, DOI 10.1112/plms/s3-15.1.61 N. K. Spanoudakis, Operators in finite distributive subspace lattices, preprint.
Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 115 (1992), 711-723
- MSC: Primary 47D30
- DOI: https://doi.org/10.1090/S0002-9939-1992-1097353-6
- MathSciNet review: 1097353