TY - JOUR
T1 - Derivations with values in ideals of semifinite von Neumann algebras
AU - Ber, A.
AU - Huang, J.
AU - Levitina, G.
AU - Sukochev, F.
N1 - Publisher Copyright:
© 2017 Elsevier Inc.
PY - 2017/6/15
Y1 - 2017/6/15
N2 - Let M be a semifinite von Neumann algebra with a faithful semifinite normal trace τ and let A be an arbitrary C⁎-subalgebra of M. Assume that E is a fully symmetric function space on (0,∞) having Fatou property and order continuous norm and E(M,τ) is the corresponding symmetric operator space. We prove that every derivation δ:A→E(M,τ):=E(M,τ)∩M is inner, strengthening earlier results by Kaftal and Weiss [28]. In the case when M is a semifinite non-finite factor, we show that our assumptions on E(0,∞) are sharp.
AB - Let M be a semifinite von Neumann algebra with a faithful semifinite normal trace τ and let A be an arbitrary C⁎-subalgebra of M. Assume that E is a fully symmetric function space on (0,∞) having Fatou property and order continuous norm and E(M,τ) is the corresponding symmetric operator space. We prove that every derivation δ:A→E(M,τ):=E(M,τ)∩M is inner, strengthening earlier results by Kaftal and Weiss [28]. In the case when M is a semifinite non-finite factor, we show that our assumptions on E(0,∞) are sharp.
KW - Derivations
KW - Ideals of τ-compact operators
KW - Schatten ideals
KW - von Neumann subalgebra
UR - http://www.scopus.com/inward/record.url?scp=85014106016&partnerID=8YFLogxK
U2 - 10.1016/j.jfa.2017.02.010
DO - 10.1016/j.jfa.2017.02.010
M3 - Article
SN - 0022-1236
VL - 272
SP - 4984
EP - 4997
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 12
ER -