Leibniz Seminorms and Best Approximation from C*-subalgebras

Details Leibniz Seminorms and Best Approximation from C*-subalgebras Leibniz Seminorms and Best Approximation from C*-subalgebras

2010-08-23

arxiv.org/abs/1008.3733v4

Sci China Math, 2011, 54(11): 2259-2274

Mathematics

Operator Algebras

24 pages. Intended for the proceedings of the conference "Operator Algebras and Related Topics". v2: added a corollary to the

Scientific paper

10.1007/s11425-011-4318-2

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.

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