منابع مشابه
Soft 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...
متن کاملB(h) Lattices, Density and Arithmetic Mean Ideals
This paper is part of an eight paper project [14]-[20] studying the arithmetic mean operator ideals in B(H) introduced by Dykema, Figiel, Weiss and Wodzicki in [10]. Every ideal I is generated by diagonal operators with positive decreasing sequences, and its arithmetic mean ideal Ia is generated by diagonal operators with the arithmetic means of those sequences. In this paper we focus on lattic...
متن کاملA Survey on the Interplay between Arithmetic Mean Ideals, Traces, Lattices of Operator Ideals, and an Infinite Schur-horn Majorization Theorem
The main result in [24] on the structure of commutators showed that arithmetic means play an important role in the study of operator ideals. In this survey we present the notions of arithmetic mean ideals and arithmetic mean at infinity ideals. Then we explore their connections with commutator spaces, traces, elementary operators, lattice and sublattice structure of ideals, arithmetic mean idea...
متن کاملDense ideals and Cardinal Arithmetic
From large cardinals we show the consistency of normal, fine, κ-complete -dense ideals on Pκ( ) for successor κ. We explore the interplay between dense ideals, cardinal arithmetic, and squares, answering some open questions of Foreman. Most large cardinals are characterizable in terms of elementary embeddings between models of set theory that have a certain amount of agreement with the full uni...
متن کاملTraces, 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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Indiana University Mathematics Journal
سال: 2011
ISSN: 0022-2518
DOI: 10.1512/iumj.2011.60.4603