非自伴算子代数的上同调群

ON THE COHOMOLOGY OF NON-SELFADJOINT OPERATOR ALGEBRAS

设H是Hilbert空间,(?)是H上的子空间格且Vφ-只有有限个.当H=V{G:G是(?)的Vφ-生成子} 时.对一切自然数n,得到Hn(M(?),B(H))= 0,其中,(?)是(?)到(?)的格同态.特别地,取(?)为恒等映射时,对完全分配的子空间格(?)有Hn(alg(?),B(H))=0.设A是完全分配的CSL代数,M是任意含A的A- 模,则Hn (A,M)= 0.

Suppose that H will denote a Hilbert space, ? will denote a subspace lattice on H, and the numbers containing V?generators are finite. when H = V{G: G is V?-generators of ?}, Hn (M?,B(H)) = 0 can be obtained for all natural numbers n, where ? is a lattice homomorphism ? into itself Especially, Hn(alg?, B(H)) = 0 exists for completely distributive subspace lattice ?. Suppose that ? is a completely distributive CSL (commutative subspace, lattice) M is any alg?-module containing alg?, then Hn[alg?,M) = 0.