We construct a complete metric space M of cardinality continuum such that every non-singleton closed separable subset fails to be Lipschitz retract M. This provides analogue the various classical and recent examples Banach spaces failing have linearly complemented subspaces prescribed smaller density character.

We study a general Kishimoto’s problem for automorphisms on simple C∗-algebras with tracial rank zero. Let A be a unital separable simple C∗-algebra with tracial rank zero and let α be an automorphism. Under the assumption that α has certain Rokhlin property, we present a proof that A ⋊α Z has tracial rank zero. We also show that if the induced map α∗0 on K0(A) fixes a “dense” subgroup of K0(A)...

In this work we describe a protocol by which two of three parties generate two bipartite entangled state among themselves without involving third party, from a non maximal W state or W type state |X〉 = α|001〉123+β|010〉123+γ|100〉123, α+ β+γ = 1 shared by three distant partners. Also we have considered the case β = γ, to obtain a range for α, for which the local output states are separable and no...

Consider these results: (a) [N. Noble, Proc. Amer. Math.Soc. 31 (1972), 613–614] every Gδ-dense subspace in a product of separable metric spaces is C-embedded; (b) [Milton Don Ulmer, Ph.D. Dissertation. Wesleyan University (Middletown, CT, USA), 1970 and Pacific J. Math. 46 (1973), 591–602] every Σproduct in a product of first-countable spaces is C-embedded; (c) [R. Pol and E. Puzio-Pol, Fund. ...