Equivalence of Projections in Involutive Rings

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Let be a ring with involution
, that is,
. An element
is called a projection if it is self-adjoint (
) and idempotent (
). The projections
and
are said to be equivalent, written
, when
exists such that
and
. Projections are algebraically equivalent if there exist
and
such that
and
.
Contributed by: Izidor Hafner (March 2018)
Open content licensed under CC BY-NC-SA
Snapshots
Details
This example and definitions were taken from [1, pp. 3–10].
References
[1] S. K. Berberian, Baer *-Rings, New York: Springer-Verlag 1972.
[2] I. Kaplansky, Rings of Operators, New York: W. A. Benjamin, 1968.
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