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May
17
reviewed Approve Why if the columns of a matrix are not linearly independent the matrix is not invertible?
May
17
reviewed Approve Vector calculus problem, constant speed, counterclockwise or clockwise.
May
17
reviewed Reject How to show that $\dfrac{\sin(x^2+y^2)}{(x^2 + y^2)^\alpha}$ integrable on $\mathbb{R}^2$
May
17
reviewed Approve How to solve nonlinear recurrence relation (quadratic)
May
8
reviewed Reject Tensor products commute with direct limits
May
8
reviewed Reject About primitive roots and square free numbers.
Apr
29
reviewed Approve Find the conjugacy classes of $A_5$
Apr
24
reviewed Approve Do all singular $n\times n$ matrices form a vector subspace when $n\ge2$?
Apr
22
reviewed Approve How to calculate the arc length of y = C/x
Apr
22
reviewed Approve Fourier Series of Complex Valued Functions
Apr
20
reviewed Approve How to solve this integral by a simple way?
Apr
20
reviewed Approve Find the function satisfying the given condition
Apr
20
reviewed Reject generating system of the kernel of a module-transformation
Apr
20
reviewed Approve An example of a continuous function such that M
Apr
2
reviewed Approve Find the arc length.
Apr
1
reviewed Approve Constructing a one-to-one correspondence between closed interval and half open interval
Mar
31
comment Commutant of algebra of multiplication operators
First of all, Proposition 5.3.2 in Pedersen is about unbounded operators and $\mathfrak A$ contains only bounded operators. But $\mathfrak A$ is just the set of self-adjoint operators $\mathfrak M_{sa}$ in the von Neumann algebra $\mathfrak M = \{M_f: f\in L_\infty(X)\}$ and, yes, there is a bijection between $\mathfrak M_{sa}$ and the real-valued functions in $L_\infty(X)$. This bijection is the restriction of the $*$-isomorphism between $\mathfrak M$ and $L_\infty(X)$ to their self-adjoint parts, where this bijection is the one guaranteed by the Borel functional calculus (Section 4.5).
Mar
31
reviewed Reject Tangential space to the rational normal curve
Mar
30
comment Commutant of algebra of multiplication operators
Your $\mathfrak A$ is basically $L^\infty(X,R)$ (the real bounded, measurable functions on $X$) acting on $L^2(X) =L^2(X,\mathbb R) + i L^2(X,\mathbb R)$. It is not a von Neumann algebra because von Neumann algebras are closed under multiplication by complex scalars and your $\mathfrak A$ is not. This suggests that it is a real von Neumann algebra?
Mar
23
reviewed Approve List all possible subgroups of $A_4.$ Determine which subgroups of $A_4$ are normal.