Algebraic Isomorphisms and Finite Distributive Subspace Lattices |
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| Authors: | Panaia Oreste |
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| Institution: | Department of Mathematics, University of Western Australia Nedlands, WA 6907, Australia, oreste{at}maths.uwa.edu.au |
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| Abstract: | Let L1 and L2 be finite distributive subspace lattices on realor complex Banach spaces. It is shown that every rank-preservingalgebraic isomorphism of AlgL1 onto AlgL2 is quasi-spatiallyinduced. If the algebraic isomorphism in question is known onlyto preserve the rank of rank one operators, then it inducesa lattice isomorphism between L1 and L2. |
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