论文标题
围绕换向器集的关闭以及$ \ Mathcal {b}（\ Mathcal {h}）$的依从元素的一组差异
Around the closures of the set of commutators and the set of differences of idempotent elements of $\mathcal{B}(\mathcal{H})$
论文作者
论文摘要
We describe the norm-closures of the set $\mathfrak{C}_{\mathfrak{E}}$ of commutators of idempotent operators and the set $\mathfrak{E} - \mathfrak{E}$ of differences of idempotent operators acting on a finite-dimensional complex Hilbert space, as well as characterising the intersection of the closures of这些设置具有$ \ Mathcal {k}（\ Mathcal {h}）$的紧凑型操作员的$ \ MATHCAL {K}（\ Mathcal {h}）$，该操作员作用于无限的，可分开的Hilbert Space。最后，我们表征了正交预测的换向器的$ \ mathfrak {c} _ {c} _ {\ mathfrak {p}} $，以及$ \ mathfrak {p} - \ mathfrak {p} - \ mathfrak {p} $ of Outthogonal projections of Orthogonal projections of Orthogonal projections of Outthogonal projections of Authogonal projections to pot of unultogonal projections。
We describe the norm-closures of the set $\mathfrak{C}_{\mathfrak{E}}$ of commutators of idempotent operators and the set $\mathfrak{E} - \mathfrak{E}$ of differences of idempotent operators acting on a finite-dimensional complex Hilbert space, as well as characterising the intersection of the closures of these sets with the set $\mathcal{K}(\mathcal{H})$ of compact operators acting on an infinite-dimensional, separable Hilbert space. Finally, we characterise the closures of the set $\mathfrak{C}_{\mathfrak{P}}$ of commutators of orthogonal projections and the set $\mathfrak{P} - \mathfrak{P}$ of differences of orthogonal projections acting on an arbitrary complex Hilbert space.
