The schur-horn theorem for operators with finite spectrum
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Dosyalar
Tarih
2014-10-01
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
American Mathematical Society
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
The carpenter problem in the context of II1 factors, formulated by Kadison, asks: Let A? M be a masa in a type II1 factor and let E be the normal conditional expectation fromMonto A. Then, is it true that for every positive contraction A in A, there is a projection P inMsuch that E(P) = A? In this note, we show that this is true if A has finite spectrum. We will then use this result to prove an exact Schur-Horn theorem for positive operators with finite spectrum in type II1 factors and an approximate Schur-Horn theorem for general positive operators in type II1 factors. © 2014 American Mathematical Society.
Açıklama
Anahtar Kelimeler
Linear Preserver, Majorization, Doubly Stochastic Matrix
Kaynak
Proceedings of the American Mathematical Society
WoS Q Değeri
Q1
