In 2006, Gudder introduced a logic order on the bounded quantum observable set S(H). In 2007, Pulmannova and Vincekova proved that for each subset D of S(H), the infimum of D exists with respect to this logic order. In this paper, we present a representation theorem for the infimum of D.

1.
S.
Gudder
,
Math. Slovaca
56
,
573
(
2006
).
2.
R.
Kadison
,
Proc. Am. Math. Soc.
2
,
505
(
1951
).
3.
T.
Moreland
and
S.
Gudder
,
Numer. Linear Algebra Appl.
286
,
1
(
1999
).
4.
S.
Gudder
,
J. Math. Phys.
37
,
2637
(
1996
).
5.
T.
Ando
,
Analytic and Geometric Inequalities and Applications
,
Mathematical Applications
Vol.
478
(
Kluwer
, Dordrecht,
1999
).
6.
D.
Hongke
,
D.
Chunyuan
, and
L.
Qihui
,
Sci. China, Ser. A: Math., Phys., Astron.
49
,
545
(
2006
).
7.
S.
Pulmannova
and
E.
Vincekova
,
Math. Slovaca
57
,
589
(
2007
).
8.
R. V.
Kadison
and
J. R.
Ringrose
,
Fundamentals of the Theory of Operator Algebra
(
Springer-Verlag
,
New York
,
1983
).
You do not currently have access to this content.