A short proof of the existence of the injective envelope of an operator space

2025/07/15 by Thomas Sinclair, Sinclair, Thomas
Mathematics · #Advanced Banach Space Theory #Holomorphic and Operator Theory #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.2507.10931

Abstract

We use Ellis' lemma to give a simple proof of the existence of the injective envelope of an operator space first shown by work of Hamana and Ruan.

Citations

• The ideal intersection property for essential groupoid C*-algebras
• Poisson boundaries of II₁ factors
• Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory
• Boundaries of reduced C*-algebras of discrete groups
• E₀-semigroups: around and beyond Arveson's work
• Weak Expectations and the Injective Envelope
• Injectivity and Projectivity in Analysis and Topology
• A Dynamical Systems Approach to the Kadison-Singer Problem
• The asymptotic lift of a completely positive map

Related

• Real structure in operator spaces, injective envelopes and G-spaces
• Multipliers of operator spaces, and the injective envelope
• Quasimultipliers of Operator Spaces
• Real Operator Algebras and Real Completely Isometric Theory
• The Jordan lattice completion and a note on injective envelopes and von Neumann algebras