Traces, ideals, and arithmetic means
نویسندگان
چکیده
منابع مشابه
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....
متن کاملTraces on Operator Ideals and Arithmetic Means
This article investigates the codimension of commutator spaces [I, B(H)] of operator ideals on a separable Hilbert space, i.e., “How many traces can an ideal support?” We conjecture that the codimension can be only zero, one, or infinity. Using the arithmetic mean (am) operations on ideals introduced in [13] and the analogous arithmetic mean operations at infinity (am-∞) that we develop extensi...
متن کاملSecond Order Arithmetic Means in Operator Ideals
We settle in the negative the question arising from [3] on whether equality of the second order arithmetic means of two principal ideals implies equality of their first order arithmetic means (second order equality cancellation) and we provide fairly broad sufficient conditions on one of the principal ideals for this implication to always hold true. We present also sufficient conditions for sec...
متن کاملTraces on Irregular Ideals
Simple answers are given to the following and related questions: For what Hubert space operator A is it true that the smallest ideal (alternatively, the smallest norm ideal, the smallest maximal norm ideal) containing A is a norm (an intermediate norm, a principal norm) ideal? Do these ideals support a nontrivial unitary invariant positive linear functional?
متن کاملSoft Ideals and Arithmetic Mean Ideals
This article investigates the soft-interior (se) and the soft-cover (sc) of operator ideals. These operations, and especially the first one, have been widely used before, but making their role explicit and analyzing their interplay with the arithmetic mean operations is essential for the study in [10] of the multiplicity of traces. Many classical ideals are “soft”, i.e., coincide with their sof...
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ژورنال
عنوان ژورنال: Proceedings of the National Academy of Sciences
سال: 2002
ISSN: 0027-8424,1091-6490
DOI: 10.1073/pnas.112074699