| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Research Abstract |
I studied operator algebras and related topics in relation to free probability theory. More precisely, I obtained the following results :(1) I gave a necessary and sufficient condition for an arbitrary free product von Neumann algebra to be a factor. More strongly, I described its central decomposition explicitly, gave an explicit description of the type I part, proved that the non-type I part always appears and becomes a type II1 or III factor, and gave an explicit algorithm for determining the type of that factor. Moreover I proved that that factor is always full.(2) I computed the Sd-andτ-invariants of any type III1 factor arising as the non-type I part of a free product von Neumann algebra.(3) I proved a very special property for weakly compact subsets in the preduals of non-commutative bounded Hardy spaces.(4) I studied the questions of factoriality, type classification and fullness for amalgamated free product von Neumann algebras, and gave several partial answers to those questions.
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