Abstract
Let A be a CSL algebra on a Hilbert space. Sufficient conditions are given so that all derivations of A into A are inner. The conditions are determined by an order relationship between the core projection of A. The proofs are based on a result of E.C. Lance which shows that the nth cohomology spaces for a nest algebra are trivial. Reflexive algebras whose invariant subspace lattice is an infinite ordinal direct sum of commutative subspace lattices satisfy the sufficient conditions. A nest subalgebra A of a von Neumann algebra which is a CSL algebra is also shown to have only inner derivations.
This research was partly supported by the NSF (USA) and the SERC (Great Britain).
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Gilfeather, F.L. (1984). Derivations on Certain CSL Algebras II. In: Butzer, P.L., Stens, R.L., Sz.-Nagy, B. (eds) Anniversary Volume on Approximation Theory and Functional Analysis. ISNM 65: International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 65. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5432-0_13
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DOI: https://doi.org/10.1007/978-3-0348-5432-0_13
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