The Hermitian part of a Rickart involution ring, I | Zendy

Jānis Cı̄rulis | Zendy

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The Hermitian part of a Rickart involution ring, I

Author(s) -

Jānis Cı̄rulis

Publication year - 2014

Publication title -

acta et commentationes universitatis tartuensis de mathematica

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.276

H-Index - 6

eISSN - 2228-4699

pISSN - 1406-2283

DOI - 10.12697/acutm.2014.18.10

Subject(s) - hermitian matrix , mathematics , pure mathematics , hilbert space , bounded function , ring (chemistry) , order (exchange) , linear operators , involution (esoterism) , algebra over a field , discrete mathematics , mathematical analysis , law , chemistry , organic chemistry , finance , economics , politics , political science

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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