trace class
41Théorème de Mercer — En mathématiques et plus précisément en analyse fonctionnelle, le théorème de Mercer est une représentation d une fonction symétrique de type positif par le carré d une série convergente de produits de fonctions. Ce théorème est l un des… …
42Mercer's theorem — In mathematics, specifically functional analysis, Mercer s theorem is a representation of a symmetric positive definite function on a square as a sum of a convergent sequence of product functions. This theorem, presented in (Mercer 1909), is one… …
43Separable states — In quantum mechanics, separable quantum states are states without quantum entanglement. Separable pure states For simplicity, the following assumes all relevant state spaces are finite dimensional. First, consider separability for pure states.… …
44Ultraweak topology — In functional analysis, a branch of mathematics, the ultraweak topology, also called the weak * topology, or weak * operator topology or sigma; weak topology, on the set B ( H ) of bounded operators on a Hilbert space is the weak * topology… …
45Ultrastrong topology — In functional analysis, the ultrastrong topology, or sigma; strong topology, or strongest topology on the set B(H) of bounded operators on a Hilbert space is the topology defined by the family of seminorms pw(x) for positive elements w of the… …
46Finite rank operator — In functional analysis, a finite rank operator is a bounded linear operator between Banach spaces whose range is finite dimensional. Finite rank operators on a Hilbert space A canonical form Finite rank operators are matrices (of finite size)… …
47Mathematical formulation of quantum mechanics — Quantum mechanics Uncertainty principle …
48Compact operator — In functional analysis, a branch of mathematics, a compact operator is a linear operator L from a Banach space X to another Banach space Y, such that the image under L of any bounded subset of X is a relatively compact subset of Y. Such an… …
49Hilbert–Schmidt operator — In mathematics, a Hilbert–Schmidt operator is a bounded operator A on a Hilbert space H with finite Hilbert–Schmidt norm, meaning that there exists an orthonormal basis {e i : i in I} of H with the property:sum {iin I} |Ae i|^2 < infty. If this… …
50Canonical ensemble — A canonical ensemble in statistical mechanics is a statistical ensemble representing a probability distribution of microscopic states of the system. The probability distribution is characterised by the proportion pi of members of the ensemble… …
