Abstract
We compute Connes-Störmer relative entropy H(M/N) for two subfactors M and N of a type II1 factor without assuming N ⊂ M. If they form a commuting square, then we have H(M/N) = H(M/M ∩ N). If their commutants form a commuting square, then we have H(M/N) = H(M ∨ N/N).
| Original language | English |
|---|---|
| Pages (from-to) | 329-341 |
| Number of pages | 13 |
| Journal | Journal of Functional Analysis |
| Volume | 133 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - Nov 1 1995 |
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All Science Journal Classification (ASJC) codes
- Analysis
Cite this
Commuting squares and relative entropy for two subfactors. / Watatani, Yasuo; Wierzbicki, Jerzy.
In: Journal of Functional Analysis, Vol. 133, No. 2, 01.11.1995, p. 329-341.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Commuting squares and relative entropy for two subfactors
AU - Watatani, Yasuo
AU - Wierzbicki, Jerzy
PY - 1995/11/1
Y1 - 1995/11/1
N2 - We compute Connes-Störmer relative entropy H(M/N) for two subfactors M and N of a type II1 factor without assuming N ⊂ M. If they form a commuting square, then we have H(M/N) = H(M/M ∩ N). If their commutants form a commuting square, then we have H(M/N) = H(M ∨ N/N).
AB - We compute Connes-Störmer relative entropy H(M/N) for two subfactors M and N of a type II1 factor without assuming N ⊂ M. If they form a commuting square, then we have H(M/N) = H(M/M ∩ N). If their commutants form a commuting square, then we have H(M/N) = H(M ∨ N/N).
UR - http://www.scopus.com/inward/record.url?scp=0011442762&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0011442762&partnerID=8YFLogxK
U2 - 10.1006/jfan.1995.1128
DO - 10.1006/jfan.1995.1128
M3 - Article
VL - 133
SP - 329
EP - 341
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
SN - 0022-1236
IS - 2
ER -