Topologically Irreducible Representations and Radicals in Banach Algebras

It is shown that the topologically irreducible representationsof a normed algebra define a certain topological radical inthe same way that the strictly irreducible representations definethe Jacobson radical and that this radical can be strictly smallerthan the Jacobson radical. An abstract theory of ‘topologicalradicals’ in topological algebras is developed and usedto relate this radical to the Baer radical (prime radical).The relations with topologically transitive representationsand standard representations in the sense of Meyer are alsoexplored. 1991 Mathematics Subject Classification: 46H15, 46H25,16Nxx.     

Measurement of the decays B--> phiK and B--> phiK*

We have observed the decays B--> phiK and phiK(*) in a sample of over 45 million B mesons collected with the BABAR detector at the PEP-II collider. The measured branching fractions are B(B+--> phiK+) = (7.7(+1.6)(-1.4)+/-0.8)x10(-6), B(B0--> phiK0) = (8.1(+3.1)(-2.5)+/-0.8)x10(-6), B(B+--> phiK(*+)) = (9.7(+4.2)(-3.4)+/-1.7)x10(-6), and B(B0--> phiK(*0)) = (8.7(+2.5)(-2.1)+/-1.1)x10(-6). We also report the upper limit B(B+--> phipi(+))<1.4x10(-6) ( 90% C.L.).     

Measurement of the B0-B-0 oscillation frequency with inclusive dilepton events

The B0-B-0 oscillation frequency has been measured with a sample of 23 x 10(6) BB- pairs collected with the BABAR detector at the PEP-II asymmetric B Factory at SLAC. In this sample, we select events in which both B mesons decay semileptonically and use the charge of the leptons to identify the flavor of each B meson. A simultaneous fit to the decay time difference distributions for opposite- and same-sign dilepton events gives deltamd = 0.493+/-0.012(stat)+/-0.009(syst) ps-1.