On Hahn-Banach type theorems for Hilbert C*-modules

Abstract

We show three Hahn-Banach type extension criteria for (sets of) bounded C*-linear maps of Hilbert C*-modules to the underlying C*-algebras of coefficients. One criterion establishes an alternative description of the property of (AW*-) C*-algebras to be monotone complete or additively complete.

16 pages, LaTeX2e, major changes and additions, updated literature list

References in corpus (4)

• Injective Envelopes of $C^{\ast }$-algebras as Operator Modules
• Injective envelopes and local multiplier algebras of C*-algebras
• A multiplier approach to the Lance-Blecher theorem
• Isomorphisms of Hilbert C*-Modules and $\ast$-Isomorphisms of Related Operator C*-Algebras

Cited by in corpus (7)

• Injective Envelopes of $C^{\ast }$-algebras as Operator Modules
• Injective envelopes and local multiplier algebras of C*-algebras
• CP-Semigroups and Dilations, Subproduct Systems and Superproduct Systems: The Multi-Parameter Case and Beyond
• Injective and projective Hilbert C*-modules, and C*-algebras of compact operators
• Kernels of Hilbert Module Maps: A Counterexample
• Regularity results for classes of Hilbert C*-modules with respect to special bounded modular functionals
• Hilbert C*-modules and related subjects - a guided reference overview I