Perfectness of certain subsemigroups of a perfect semigroup

An Example of a Positive Semidefinite Double Sequence Which is Not a Moment Sequence

“…The non-semiperfectness of S was shown by Nakamura and Sakakibara [7]. We shall show that if γ is the positive solution to the …”

A reduction of the problem of characterizing perfect semigroups

“…In [4], Theorem, it was shown that if S is a (Radon) perfect semigroup with zero and if T is a * -subsemigroup of S containing 0 and such that T \ {0} is an ideal of S then T is likewise (Radon) perfect. The following result seems to be the closest analogue of this for semigroups without zero.…”

“…The following result seems to be the closest analogue of this for semigroups without zero. The proof, like the proof of Theorem 2.3, is strongly inspired by the argument in [4].…”

Extensions of results of Herglotz, Hamburger, and Sz.-Nagy on the representation of positive semideænite functions as integrals of hermitian multiplicative functions

“…Indeed, if S is as in the last Theorem of the present paper then S is a completely semiperfect semigroup which is the union of a semilattice of Ã-semigroups, two of which are isomorphic to f0g and N 2 f2Y 3Y 4Y F F Fg, respectively. Now the set ff0gY N 2 g is not an O-class since if it were then the semigroup f0g N 2 N 0 nf1g would be semiperfect, which it is not (Nakamura and Sakakibara [16]). Assume…”

“…By an argument inspired by Nakamura and Sakakibara [16], one next shows that for each t e T there is a unique measure m t e F 1 U H t Y C d , each entry of which has an L 2 -density with respect to trl t , such that…”