Let X be a Hilbert C*-module over a C*-algebra B. In this paper we introduce two classes of opera... more 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.
Let Alg 𝒩 be a nest algebra associated with the nest 𝒩 on a (real or complex) Banach space 𝕏. Sup... more Let Alg 𝒩 be a nest algebra associated with the nest 𝒩 on a (real or complex) Banach space 𝕏. Suppose that there exists a non-trivial idempotent P ∈ Alg 𝒩 with range P (𝕏) ∈ 𝒩, and δ : Alg 𝒩 → Alg 𝒩 is a continuous linear mapping (generalized) left derivable at P, i.e. δ (ab) = aδ (b) + bδ (a) (δ (ab) = aδ(b) + bδ(a) − baδ(I)) for any a, b ∈ Alg 𝒩 with ab = P, where I is the identity element of Alg 𝒩. We show that is a (generalized) Jordan left derivation. Moreover, in a strongly operator topology we characterize continuous linear maps on some nest algebras Alg 𝒩 with the property that δ (P ) = 2Pδ (P ) or δ (P ) = 2P δ (P ) − Pδ (I) for every idempotent P in Alg 𝒩.
Let X be a Hilbert C*-module over a C*-algebra B. In this paper we introduce two classes of opera... more 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.
Let Alg 𝒩 be a nest algebra associated with the nest 𝒩 on a (real or complex) Banach space 𝕏. Sup... more Let Alg 𝒩 be a nest algebra associated with the nest 𝒩 on a (real or complex) Banach space 𝕏. Suppose that there exists a non-trivial idempotent P ∈ Alg 𝒩 with range P (𝕏) ∈ 𝒩, and δ : Alg 𝒩 → Alg 𝒩 is a continuous linear mapping (generalized) left derivable at P, i.e. δ (ab) = aδ (b) + bδ (a) (δ (ab) = aδ(b) + bδ(a) − baδ(I)) for any a, b ∈ Alg 𝒩 with ab = P, where I is the identity element of Alg 𝒩. We show that is a (generalized) Jordan left derivation. Moreover, in a strongly operator topology we characterize continuous linear maps on some nest algebras Alg 𝒩 with the property that δ (P ) = 2Pδ (P ) or δ (P ) = 2P δ (P ) − Pδ (I) for every idempotent P in Alg 𝒩.
Uploads
Papers by saman sattari