Sentence examples for minimal operator space from inspiring English sources

Our technique involves introducing a numerical invariant α(X) for a normed space X which measures the difference between the minimal operator space structure which can be assigned to X, MIN X), and the maximal structure, MAX X).

We show that the matrix norms that define the k-minimal operator spaces are equal to a family of norms that have been studied independently as a tool for detecting k-positive linear maps and bound entanglement.

We examine k-minimal and k-maximal operator spaces and operator systems, and investigate their relationships with the separability problem in quantum information theory.

In general, under a certain definiteness condition, a formally differential expression can generate a minimal operator in a related Hilbert space and its adjoint is the corresponding maximal operator (see, e.g., [7, 8]).

In particular, the maximal operator corresponding to Eq. (1.1) is multi-valued, and the minimal operator is non-densely defined in the related Hilbert space (cf. [23]).

Using this Archimedean order unit space, for a fixed k∈N we construct a super k-minimal operator system OMINk(S) and a super k-maximal operator system OMAXk(S), which are the general versions of the minimal operator system OMIN(S) and the maximal operator system OMAX(S) introduced recently, such that for k="1 we obtain the equality, respectively.

Also, segmentations have to be robust and involve minimal operator input.

Note that for a symmetric linear difference equation, its minimal operator may not be densely defined, and its minimal and maximal operators may be multi-valued (cf. [10 12]).

The convertible top goes up and down manually, but gracefully, with minimal operator effort.

Finally, it should be able to segment data reliably without or only with minimal operator intervention.

The minimal operators generated by Sturm-Liouville and some higher-order differential and difference expressions with complex coefficients are J-symmetric operators in the related Hilbert spaces (e.g., [2 4]).