Derivations and isomorphisms of certain reflexive operator algebras |
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| Authors: | Hou Chengjun Han Deguang |
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| Institution: | (1) Department of Mathematics, Qufu Normal University, 273165 Qufu, China;(2) Institute of Mathematics, Fudan University, 200433 Shanghai, China;(3) Department of Mathematics, Qufu Normal University, 273165 Qufu, China |
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| Abstract: | In this paper, we will prove that every derivation of completely distributive subspace lattice (CDS) algebras on Banach space
is automatically continuous. This is new even in the Hilbert space case. As an application of this result, we obtain that
every additive derivation of nest algebras on Banach spaces is inne. We will also prove that every isomorphism between nest
algebras on Banach space is automatically continuous, and in addition, is spatial.
Research supported by NSF of China and YSF of Shandong |
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| Keywords: | CDS algebra Nest algebra Derivation Isomorphism |
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