query: Product of two positive compact, self adjoint operators
positive_passages.docid: 20309
positive_passages.text: Product and sum of positive operators is positive
negative_passages.docid: 71316
negative_passages.text: Two inner products being equal up to a scalar
negative_passages.docid: 119775
negative_passages.text: Density of finite rank operator in compact operators on Hilbert spaces
negative_passages.docid: 146730
negative_passages.text: The adjoint of left exterior multiplication by $\xi$ for hodge star operator
negative_passages.docid: 155123
negative_passages.text: Selfadjoint Operator: Basic Criterion
negative_passages.docid: 86481
negative_passages.text: Let $H$ be an infinite-dimensional separable Hilbert space, show that a Hilbert-Schmidt operator is compact
negative_passages.docid: 81040
negative_passages.text: proof about commutative operators and T-cyclic vectors
negative_passages.docid: 22394
negative_passages.text: Compact operator maps weakly convergent sequences into strongly convergent sequences
negative_passages.docid: 129549
negative_passages.text: Showing that the orthogonal projection in a Hilbert space is compact iff the subspace is finite dimensional
negative_passages.docid: 11109
negative_passages.text: The ideal generated by a non-compact operator
negative_passages.docid: 55067
negative_passages.text: Norm of self-adjoint operator
negative_passages.docid: 87119
negative_passages.text: A positive "Fourier transform" is integrable
negative_passages.docid: 14084
negative_passages.text: The Multiplier Algebra of the Hardy Hilbert Space
negative_passages.docid: 9268
negative_passages.text: Proving that the Union of Two Compact Sets is Compact
negative_passages.docid: 11159
negative_passages.text: Problem about a compact operator $T:l^p\rightarrow l^p$
negative_passages.docid: 140756
negative_passages.text: Image of closed unit ball under a compact operator
negative_passages.docid: 108657
negative_passages.text: Cross product of the quantum mechanical operators $\textbf{p}$ and $\textbf{A}$