18 research outputs found
Majorization and arithmetic mean ideals
Following "An infinite dimensional Schur-Horn theorem and majorization
theory", Journal of Functional Analysis 259 (2010) 3115-3162, this paper
further studies majorization for infinite sequences. It extends to the infinite
case classical results on "intermediate sequences" for finite sequence
majorization. These and other infinite majorization properties are then linked
to notions of infinite convexity and invariance properties under various
classes of substochastic matrices to characterize arithmetic mean closed
operator ideals and arithmetic mean at infinity closed operator ideals.Comment: To appear in Indiana University Mathematics Journa
Traces, ideals, and arithmetic means
This article grew out of recent work of Dykema, Figiel, Weiss, and Wodzicki (Commutator structure of operator ideals) which inter alia characterizes commutator ideals in terms of arithmetic means. In this paper we study ideals that are arithmetically mean (am) stable, am-closed, am-open, soft-edged and soft-complemented. We show that many of the ideals in the literature possess such properties. We apply these notions to prove that for all the ideals considered, the linear codimension of their commutator space (the ânumber of traces on the idealâ) is either 0, 1, or â. We identify the largest ideal which supports a unique nonsingular trace as the intersection of certain Lorentz ideals. An application to elementary operators is given. We study properties of arithmetic mean operations on ideals, e.g., we prove that the am-closure of a sum of ideals is the sum of their am-closures. We obtain cancellation properties for arithmetic means: for principal ideals, a necessary and sufficient condition for first order cancellations is the regularity of the generator; for second order cancellations, sufficient conditions are that the generator satisfies the exponential Î(2)-condition or is regular. We construct an example where second order cancellation fails, thus settling an open question. We also consider cancellation properties for inclusions. And we find and use lattice properties of ideals associated with the existence of âgaps.
Verification criteria on the reliability of personal dosimetric services from x and gamma radiations
The paper presents the methods used by Working Group ENEA-EDP (Experts in Personal Dosimetry) to control the reliability of the Dosimetric Services operating in Italy and asking for the above controls on voluntary basis. Testing and irradiation test methods are explained as well as the evaluation criteria. The paper includes suggestions and guide-lines to gain the status of 'Reliable Service'. Technical equipment and operating procedures needed to pass the test are also illustrated