A Cohomological Property of pi-invariant Elements

作者：Filali M^*; Monfared M Sangani

来源：Canadian Mathematical Bulletin, 2013, 56(3): 534-543.

DOI：10.4153/CMB-2011-184-7

• Banach algebras
• pi-invariance
• derivations
• representations

Let A be a Banach algebra and let pi : A -%26gt; L(H) be a continuous representation of A on a separable Hilbert space H with dim H = m. Let pi(ij) be the coordinate functions of pi with respect to an orthonormal basis and suppose that for each 1 %26lt;= j %26lt;= m, C-j = Sigma(m)(i=1) parallel to pi(ij)parallel to(A*) %26lt; infinity and sup (j) C-j %26lt; infinity. Under these conditions, we call an element (Phi) over bar is an element of l(infinity) (m, A** )left pi-invariant if a . (Phi) over bar = t(pi)(a)(Phi) over bar for all a is an element of A. In this paper we prove a link between the existence of left pi-invariant elements and the vanishing of certain Hochschild cohomology groups of A. Our results extend an earlier result by Lau on F-algebras and recent results of Kaniuth, Lau, Pym, and and the second author in the special case where pi : A -%26gt; C is a non-zero character on A.

• 出版日期2013-9