Leibniz Seminorms and Best Approximation from C*-subalgebras

Abstract

We show that if B is a C*-subalgebra of a C*-algebra A such that B contains a bounded approximate identity for A, and if L is the pull-back to A of the quotient norm on A/B, then L is strongly Leibniz. In connection with this situation we study certain aspects of best approximation of elements of a unital C*-algebra by elements of a unital C*-subalgebra.

24 pages. Intended for the proceedings of the conference "Operator Algebras and Related Topics". v2: added a corollary to the main theorem, plus several minor improvements v3: much simplified proof of a key lemma, corollary to main theorem added v4: Many minor improvements. Section numbers increased by 1

References in corpus (2)

• Leibniz seminorms for "Matrix algebras converge to the sphere"
• Non-Commutative Metrics on Matrix State Spaces

Cited by in corpus (6)

• Curved Noncommutative Tori as Leibniz Quantum Compact Metric Spaces
• Birkhoff-James orthogonality and applications : A survey
• Best approximations, distance formulas and orthogonality in C*-algebras
• AF algebras in the quantum Gromov-Hausdorff propinquity space
• Pythagoras Theorem in Noncommutative Geometry
• A characterization of Hermitian matrices with variable diagonal and smallest operator norm