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Suppose B is a trivial bundle whose fibers are type I2 factors and p is a constant section of B corresponding to some projection with 1-dimensional image. Projections with 1-dimensional image in a ty …

No. Take any automorphism in the Tomita-Takesaki modular flow of M. It is well known that an automorphism in the modular flow is inner if and only if M is semifinite.

Such t_0 is unique if its support is at most p, where p is the support of ϕ. Note that we can replace t_0 by pt_0p and the support of pt_0p is at most p. Without this additional condition t_0 is high …

Morphisms of von Neumann algebra have very nice properties. More precisely, the kernel of a morphism f: M→N of von Neumann algebras is a σ-weakly closed two-sided ideal. Such ideals are in bijective c …

If by a normal character you mean a normal morphism of C*-algebras A→C, then every commutative von Neumann algebra canonically decomposes as a product of its atomic and diffuse parts, the atomic part …

Yes. The kernel of F is an ultraweakly closed *-ideal of M generated by some central projection z. M splits as a direct sum of zM and (1-z)M. As a 2x2 matrix F has only two nonzero entries, one that …

This follows from the reduction theory for von Neumann algebras (alias direct integral decomposition). Any von Neumann algebra is a direct integral of factors (i.e., von Neumann algebras with a trivia …

No. Take e=0 and 0 < f < 1 such that both f and 1−f are infinite, with (1−f)~1. Then e≾f because 0≾f for any projection f. Also 1−e≾1−f because 1≾1−f, which holds by definition of f.

A von Neumann algebra is a $C^*$-algebra $A$ that admits a predual, i.e., a Banach space $A_*$ such that there is an isomorphism $A\to(A_*)^*$. A morphism of von Neumann algebras is a morphism of $C^ …

How the norm on L^{P} space related to weight φ? The L^p-spaces and their norms are independent of the choice of the weight φ. See, for instance, the exposition by Yamagami in “Algebraic Aspects …

This is false. Consider, for example, the case of M being the von Neumann algebra of bounded complex-valued functions on an infinite countable set I. It acts on the Hilbert space of square-summable fu …

The category of von Neumann algebras W* admits a variety of monoidal structures of three distinct flavors. (1) W* is complete and therefore you have a monoidal structure given by the categorical prod …

There is a notion of compact element for any W*-algebra, namely, the two-sided ideal of compact elements is the norm-closure of the two-sided ideal of finite-rank elements, the latter being defined as …

This question has at least 3 answers: 1) Given a von Neumann algebra M, take its canonical L^2-space L^2(M), which is a Hilbert space, take the corresponding canonical representation of M on L^2(M) vi …

Blackadar in his textbook on operator algebras gives a complete classification of norm-closed ideals in factors. See Proposition III.1.7.11.