The first cohomology group of some operator algebras on Hilbert C*-modules

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Abstract Let X be a Hilbert C*-module over a C*-algebra B. In this paper we introduce two classes of operator algebras on the Hilbert C*-module X called operator algebras with property and operator algebras with property ℤ, and we study the first (continuous) cohomology group of them with coefficients in various Banach bimodules under several conditions on B and X. Some of our results generalize the previous results. Also we investigate some properties of these classes of operator algebras.