If $(pi_λ)_λinmathbb R$ is a family of orthogonal projections, do $λ↦left|pi_λxright|_H^2$ and $λ↦pi_λx$ have the same variation? Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 23, 2019 at 23:30 UTC (7:30pm US/Eastern)Extending the domain of the Dirichlet form associated with a symmetric Markov semigroupLet three signed measures such that $lambda_1botmu$ and $lambda_2botmu$, then $left(lambda_1+lambda_2right)botmu$?Show that an operator is self-adjointShow that the eigenvalues of a compact and self-adjoint bounded linear operator are summableIf $B:X×Y→Z$ is bounded and bilinear, $A:Xto Y$ is nuclear and $(e_n)$ is an ONB, are we able to show $sum_n=1^∞left|B(e_n,Ae_n)right|_Z<∞$?If $(H_λ)_λ≥0$ is a spectral decomposition and $π_λ$ is the orthogonal projection onto $H_λ$, then $t↦π_λ$ is increasing and right-continuousIntegrability with respect to a spectral measureSome questions about the spectral composition of a nonnegative self-adjoint operatorShow that the operator associated to a spectral decomposition on a Hilbert space is self-adjointWhat is the usual definition of the spectral measure for a nonnegative self-adjoint operator on a Hilbert space?Norm of the sum of orthogonal projections
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