All Questions

A $\mathrm{C}^*$-algebra $\mathcal{A}\subset B(\mathsf{H})$ is a norm-closed, self-adjoint subalgebra of bounded operators on a Hilbert space. If we then take a unital self-adjoint (possibly closed) ...

It was mentioned on Page 916 Problem 7 of Halmos's "Ten Problems in Hilbert space" that there is a proof for "Every compact quasinilpotent operator is the limit of nilpotent ones" ...

Let $T_+$ be the set of a positive trace-class operators over some separable Hilbert space and $A: T_+ \to \mathbb{R}\cup \{\infty\}$ some linear functional. In general, $A$ will not be continuous. ...

Let $H$ be a Hilbert space, $T_+(H)$ the set of positive self-adjoint trace-class operators on $H$, and $f : T_+(H) \to [0,m]$ a non-negative, bounded, convex functional. I don't necessarily know that ...

Is the spectral theorem for self-adjoint compact operators on a Hilbert space also true if the Hilbert space is real (instead of complex)? Wikipedia says this is true. However, it seems to me that ...