Absolutely compatible pair of elements in a von Neumann algebra-II
Abstract
Let A be a unital C*-algebra with unity 1A. A pair of elements 0 a, b 1A in A is said to be absolutely compatible if, a - b + 1A - a - b = 1A. In this paper we provide a complete description of absolutely compatible pair of strict elements in a von Neumann algebra. The end form of such a pair has a striking resemblance with that of a `generic pair' of projections on a complex Hilbert space introduced by Halmos.
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