Some examples of lifting problems from quotient algebras
Abstract
We consider three lifting questions: Given a C*-algebra I, if there is a unital C*-algebra A contains I as an ideal, is every unitary from A/I lifted to a unitary in A? is every unitary from A/I lifted to an extremal partial isometry? is every extremal partial isometry from A/I lifted to an extremal partial isometry? We show several constructions of I which serve as working examples or counter-examples for above questions.
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