ELEMENTARY PROOF OF SCHWEITZER'S THEOREM ON HILBERT C^*-MODULES IN WHICH ALL CLOSED SUBMODULES ARE ORTHOGONALLY CLOSED

スポンサーリンク

概要

• 論文の詳細を見る

• Let A and B be C*-algebras and let X be an A-B-imprimitivity bimodule. Schweitzer showed the theorem that if every closed right B-submodule of X is orthogonally closed, then there are families {H_i}_<iEI>, {K_i}_<iEI> of Hilbert spaces such that A (resp. B) is isomorphic to the C_0-direct sum Σ^*_<iEI>C(H_i) of all compact operators C(H_i) on H_I (resp. Σ^*_<iEI>C(K_i) of all compact operators C(K_i) on K_i) as a C^*-algebra, and X is isomorphic to the C_0-direct sum Σ^*_<iEI>C(K_i, H_i) as a Hilbert C^*-module, where C(K_i,H_i) denotes the Hilbert C^*-module consisting of all compact operators from K_i into H_i. In this paper, we give an alternative proof, of this theorem, which is shorter and more elementary than the original one.

• 関西大学の論文
• 2005-03-21

著者

• Kusuda Masaharu

  Department Of Mathematics

• Kusuda Masaharu

  Department De Mathematiques Faculte De Technologie Universite Ansai

関連論文

• Weak expectations in C*-dynamical systems
• CARACTERISATION DES FORMES LINEAIRES NORMALES INVARIANTES SUR LES ALGEBRES DE VON NEUMANN ET LEURS PROLONGEMENTS INVARIANTS
• ELEMENTARY PROOF OF SCHWEITZER'S THEOREM ON HILBERT C^*-MODULES IN WHICH ALL CLOSED SUBMODULES ARE ORTHOGONALLY CLOSED
• $G$-Central States of Almost Periodic Type on $C\sp *$-Algebras
• AN ALTERNATIVE PROOF OF THE DUALITY THEOREM FOR CROSSED PRODUCTS OF HILBERT C^*-MODULES BY ABELIAN GROUP ACTIONS

スポンサーリンク