The Hermitian part of a Rickart involution ring, I

  • Jānis Cīrulis Institute of Mathematics and Computer Science, University of Latvia, LV-1459 Riga
Keywords: Hermitian part, involution ring, logical order, partial ring, projection, self-adjoint operator


Rickart *-rings may be considered as a certain abstraction of the rings B(H) of bounded linear operators of a Hilbert space H. In 2006, S. Gudder introduced and studied a certain ordering (called the logical order) of self-adjoint Hilbert space operators; the set S(H) of these operators, which is a partial ring, may be called the Hermitian part of B(H). The new order has been further investigated also by other authors. In this first part of the paper, an abstract analogue of the logical order is studied on certain partial rings that approximate the Hermitian part of general *-rings; the special case of Rickart *-rings is postponed to the next part.


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