Continuity of positive functionals on topological 1-algebras |
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Authors: | David L Johnson |
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Affiliation: | Department of Mathematics, University of Arkansas, Fayetteville, Arkansas 72701 U.S.A. |
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Abstract: | It is shown that the set m × n of complex m × n matrices forms a lower semilattice under the partial ordering A ? B defined by denotes the conjugate transpose of A. As a special case of a result for division rings, it is further shown that, over any field F, form = n = 2 and any proper involution 1 of F2 × 2, the corresponding intersections A ∩ B all exist. |
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