All Questions

Let $H$ a Hilbert space, and $\mathcal C$ an arbitrary set of closed subspaces of $H$. Is it true that $$\left( \bigcap_{Z\in \mathcal C}Z\right)^\perp = \overline{\sum_{Z\in \mathcal C} Z^\perp}$$ ...

In my paper On the optimal error bound for the first step in the method of cyclic alternating projections, I defined functions $f_n:[0,1]\to\mathbb{R}$, $n\geqslant 2$, by $$ f_n(c)=\sup\{\|P_n\dotsm ...

The Calkin algebra $C(H)$ is the quotient of $B(H)$, the ring of bounded linear operators on a separable infinite-dimensional Hilbert space $H$, by the ideal $K(H)$ of compact operators. In 1977, ...

I have a simple question I've managed to get myself quite confused about. Given a Hilbert space H, what do we know about the cardinality of (a) the set $P(H)$ of projection operators onto $H$ (...