On the geometry of the algebraic Davis--Wielandt shell and norm-parallelism in C*-algebra
Abstract
This article is devoted to the study of the Davis--Wielandt shell and the Davis--Wielandt radii of elements in a C*-algebra. Utilizing a state-space approach, several geometric properties of the algebraic Davis--Wielandt shell are established. Upper and lower bounds for the algebraic Davis--Wielandt radii are obtained including the Davis--Wielandt radius of the sum of k elements. We also explore the relationship between norm-parallelism and the Davis--Wielandt radii of elements.
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