query: Given two non-commuting linear operators prove that at least one is discontinuous
positive_passages.docid: 127121
positive_passages.text: The identity cannot be a commutator in a Banach algebra?
negative_passages.docid: 109512
negative_passages.text: Let f,g be bilinear forms on a finite dimensional vector space. Show that there exist unique linear operators
negative_passages.docid: 7358
negative_passages.text: For each $y \in \mathbb{R}$ either no $x$ with $f(x) = y$ or two such values of $x$. Show that $f$ is discontinuous.
negative_passages.docid: 14111
negative_passages.text: Determining possible minimal polynomials for a rank one linear operator
negative_passages.docid: 73406
negative_passages.text: Prove that $E_{\lambda}(T)=E_{\lambda^{-1}}(T^{-1})$ if $T$ is an invertible linear operator on a finite dimensional vector space $V$
negative_passages.docid: 123149
negative_passages.text: Prove that $E$ is disconnected iff there exists two open disjoint sets $A$,$B$ in $X$
negative_passages.docid: 62999
negative_passages.text: Linear functional on a Banach space is discontinuous then its nullspace is dense.
negative_passages.docid: 135661
negative_passages.text: Weakly continuous operators are continuous
negative_passages.docid: 121802
negative_passages.text: Prove that every self-adjoint unitary linear operator can be expressed in the form $U\alpha = \beta - \gamma$
negative_passages.docid: 51302
negative_passages.text: Show that the operator norm is submultiplicative
negative_passages.docid: 45071
negative_passages.text: Having the derivative be an operator
negative_passages.docid: 56102
negative_passages.text: Prove that there is no non-zero linear operator on $\mathbb C^{2}$ such that $(\alpha | T\alpha) = 0$
negative_passages.docid: 45363
negative_passages.text: Show that both mixed partial derivatives exist at the origin but are not equal
negative_passages.docid: 151347
negative_passages.text: Why do operators belonging to different Hilbert spaces commute?
negative_passages.docid: 158343
negative_passages.text: how to prove an element is non-zero in a tensor-product
negative_passages.docid: 54668
negative_passages.text: Proof for the completeness of eigenfunctions of a self-adjoint operator
negative_passages.docid: 70606
negative_passages.text: Show that the LU decomposition of matrices of the form $\left[\begin{smallmatrix}0& x\\0 & y\end{smallmatrix}\right]$ is not unique