query: "well-known" inequality for numerical radius of an operator
positive_passages.docid: 154226
positive_passages.text: Upper bound for norm of Hilbert space operator
negative_passages.docid: 106815
negative_passages.text: Better bound for integral inequality
negative_passages.docid: 95030
negative_passages.text: Proving the Cauchy-Schwarz inequality by induction
negative_passages.docid: 98242
negative_passages.text: Integral inequality in $\Bbb R^n$
negative_passages.docid: 62425
negative_passages.text: Equivalent Definitions of the Operator Norm
negative_passages.docid: 19078
negative_passages.text: Prove an interpolation inequality
negative_passages.docid: 157328
negative_passages.text: A complex analysis problem to prove an inequality
negative_passages.docid: 65062
negative_passages.text: Prove $\text{rank}(A) \geq \frac{(\text{tr}(A))^2}{\text{tr}(A^2)}$ when $A$ is Hermitian
negative_passages.docid: 24925
negative_passages.text: Recurrence Inequality
negative_passages.docid: 100731
negative_passages.text: Positive operator has a positive spectrum?
negative_passages.docid: 158082
negative_passages.text: Is $\|A^n\|=\|A\|^n$ true for any normal operator in a Hilbert space?
negative_passages.docid: 156858
negative_passages.text: Kernel of powers of a normal operator
negative_passages.docid: 95901
negative_passages.text: Inequality similar to the Schwarz-Pick theorem
negative_passages.docid: 31302
negative_passages.text: Hilbert Schmidt Norm-Rank-inequality
negative_passages.docid: 88535
negative_passages.text: Relation between the distance from a point to the resolvent set of a self-adjoint operator and the norm of a related operator
negative_passages.docid: 71371
negative_passages.text: Nonnegativity of integral, integral operator
negative_passages.docid: 87494
negative_passages.text: $\operatorname{rank}(T^3) + \operatorname{rank}(T) \geq 2\operatorname{rank}(T^2)$ for finite-dimensional $V$