Everything about Affiliated operator
In mathematics, affiliated operators were introduced by Murray and von Neumann in the theory of von Neumann algebras as a technique for using unbounded operators to study modules generated by a single vector. Later Atiyah and Singer showed that index theorems for elliptic operators on closed manifolds with infinite fundamental group could naturally be phrased in terms of unbounded operators affiliated with the von Neumann algebra of the group. Algebraic properties of affiliated operators have proved important in L2 cohomology, an area between analysis and geometry that evolved from the study of such index theorems. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Affiliated operatorA 5-minute orientation
- Pick up a classic book: United NationsThe most-reprinted book on the subject
- Read the landmark paper: $$L_1$$ L 1 -space for a positive operator affiliated with von Neumann algebraCited 7 times
- Go sideways: Commutation theorem for tracesA closely related topic
- Go sideways: Abelian von Neumann algebraA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
$$L_1$$ L 1 -space for a positive operator affiliated with von Neumann algebra
Renormalizations of measurable operator ideal spaces affiliated to semi-finite von Neumann algebra
Geometric Properties of Harmonic Function Affiliated With Fractional Operator
Relative commutant of an unbounded operator affiliated with a finite von Neumann algebra
📚 Books worth reading
- 📕United NationsUnited States. General Accounting Office · 1987
- 📕Foreign direct investment in the United StatesUnited States. Bureau of Economic Analysis · 1985
- 📕Foreign Direct Investment in the United StatesCommerce Department Stafff · 1996
- 📕Reducing operating costs in affiliated produce warehousesArnold L. Lundquist · 1966
- 📕Co-operative development of library services in affiliated colleges of the Victoria Institute of CollegesJ. I. Horacek · 1974
Foreign Direct Investment in the United StatesEconomic Analysis Bureau (U.S.) · 1999- 📕Survey of corporate philanthropy at Japanese-affiliated operations in the United StatesNihon Bōeki Shinkōkai · 1995
- 📕U.S.-Brazil business listing · 1980
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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