Automorphic images of commutative subspace lattices

Authors:
K. J. Harrison and W. E. Longstaff

Journal:
Trans. Amer. Math. Soc. **296** (1986), 217-228

MSC:
Primary 46C10; Secondary 06B99, 47A15, 47D25

DOI:
https://doi.org/10.1090/S0002-9947-1986-0837808-1

MathSciNet review:
837808

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Abstract | References | Similar Articles | Additional Information

Abstract: Let denote the lattice of all (closed) subspaces of a complex, separable Hilbert space . Let be the following condition that a subspace lattice may or may not satisfy: (AC)

**[1]**W. B. Arveson,*Operator algebras and invariant subspaces*, Ann. of Math. (2)**100**(1974), 433-532. MR**0365167 (51:1420)****[2]**W. G. Bade,*Weak and strong limits of spectral operators*, Pacific J. Math.**4**(1954), 393-413. MR**0063567 (16:144a)****[3]**-,*On Boolean algebras of projections and algebras of operators*, Trans. Amer. Math. Soc.**80**(1955), 345-360. MR**0073954 (17:513d)****[4]**R. Baer,*Linear algebra and projective geometry*, Academic Press, New York, 1952. MR**0052795 (14:675j)****[5]**J. B. Conway,*A complete Boolean algebra of subspaces which is not reflexive*, Bull. Amer. Math. Soc.**79**(1973), 720-722. MR**0320778 (47:9312)****[6]**K. R. Davidson,*Commutative subspace lattices*, Indiana Univ. Math. J. (3)**27**(1978), 479-490. MR**0482264 (58:2340)****[7]**T. Donnellan,*Lattice theory*, Pergamon Press, London, 1968. MR**0233738 (38:2059)****[8]**N. Dunford and J. T. Schwartz,*Linear operators*. Part III:*Spectral operators*, Wiley, New York, 1971. MR**1009164 (90g:47001c)****[9]**P. A. Fillmore and W. E. Longstaff,*On isomorphisms of lattices of closed subspaces*, Canad. J. Math. (5)**36**(1984), 820-829. MR**762744 (86c:46012)****[10]**P. R. Halmos,*Reflexive lattices of subspaces*, J. London Math. Soc.**4**(1971), 257-263. MR**0288612 (44:5808)****[11]**A. Hopenwasser,*The equation**in a reflexive operator algebra*, Indiana Univ. Math. J. (1)**29**(1980), 121-126. MR**554821 (81c:47014)**

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DOI:
https://doi.org/10.1090/S0002-9947-1986-0837808-1

Article copyright:
© Copyright 1986
American Mathematical Society