A reflexivity criterion for Hilbert C*-modules over commutative C*-algebras

作者：Frank Michael^*; Manuilov Vladimir; Troitsky Evgenij

来源：The New York Journal of Mathematics, 2010, 16: 399-408.

• Hilbert C*-module
• reflexivity
• commutative C*-algebra

A C*-algebra A is C*-reflexive if any countably generated Hilbert C*-module M over A is C*-reflexive, i.e., the second dual module M '' coincides with M. We show that a commutative C*-algebra A is C*-reflexive if and only if for any sequence I-k of mutually orthogonal nonzero C*-subalgebras, the canonical inclusion circle plus I-k(k) subset of A doesn't extend to an inclusion of Pi(k) I-k.

• 出版日期2010
• 单位哈尔滨工业大学