A lower bound on the amount of noise that must be added to a GHZ-like entangled state to make it separable (also called the random robustness) is found using the transposition condition. The bound is applicable to arbitrary numbers of subsystems, and dimensions of Hilbert space, and is shown to be exact for qubits. The new bound is compared with previous such bounds on this quantity, and found ...

Let G be a semisimple algebraic group over a local field K of characteristic p. If the universal covering map Gsc → G is inseparable then no open subgroup of G(K) is finitely generated. Otherwise, for any compact open subgroup G with probability 1 two randomly chosen elements generate an open subgroup of G(K). Our main tool is a recent theorem by R. Pink characterizing compact groups linear ove...

We prove that a Schauder frame for any separable Banach space is shrinking if and only if it has an associated space with a shrinking basis, and that a Schauder frame for any separable Banach space is shrinking and boundedly complete if and only if it has a reflexive associated space. To obtain these results, we prove that the upper and lower estimate theorems for finite dimensional decompositi...

This paper first improves Chen and Hsieh’s definition of generalized fuzzy numbers, which makes it the generalization of definition of fuzzy numbers. Secondly, in terms of the generalized fuzzy numbers set, we introduce two different kinds of orders and arithmetic operations and metrics based on the λ-cutting sets or generalized λ-cutting sets, so that the generalized fuzzy numbers are integrat...

Given a map T : X → X on a set X we examine under what conditions there is a separable metrizable or an hereditarily Lindelöf or a Lindelöf topology on X with respect to which T is a continuous map. For separable metrizable and hereditarily Lindelöf, it turns out that there is a such a topology precisely when the cardinality ofX is no greater than the cardinality of the continuum. We go onto pr...

We prove that a space is quotient π-image of a locally separable metric space if and only if it has a πand double cs∗cover. We also investigate quotient π-s-images of locally separable metric spaces.

If a separable Banach space X is such that for some nonquasireflexive Banach space Y there exists a surjective strictly singular operator T : X → Y then for every countable ordinal α the dual of X contains a subspace whose weak∗ sequential closures of orders less than α are not norming over any infinite-dimensional subspace of X and whose weak∗ sequential closure of order α+ 1 coincides with X∗...

We characterize those classes C of separable Banach spaces for which there exists a separable Banach space Y not containing l1 and such that every space in the class C is a quotient of Y .