Absolute Continuity in Noncommutative Measure Theory

作者：Hamhalter Jan^*

来源：International Journal of Theoretical Physics, 2010, 49(12): 3139-3145.

DOI：10.1007/s10773-009-0105-z

• Von Neumann algebras
• Absolute continuity of operators
• Vitali-Hahn-Saks
• Theorem

Recent results on absolute continuity of Banach space valued operators and convergence theorems on operator algebras are deepened and summarized It is shown that absolute continuity of an operator T on a von Neumann algebra M with respect to a positive normal functional psi on M is not implied by the fact that the null projections of psi are the null projections of T However, it is proved that the implication above is true whenever M is finite or T is weak*-continuous Further it is shown that the absolute value preserves the Vitali-Hahn-Saks property if, and only if, the underlying algebra is finite This result Improves classical results on weak compactness of sets of noncommutative measures

• 出版日期2010-12