… Pimsner–Popa basis for II 1 factor inclusions is automatically a basis according to our notion…
Also, motivated by [11] and [9], Watatani [15] has introduced what he calls ‘quasi-basis for …

We first discuss the methods introduced by the authors (Ann. Sci. Ecole Norm. Sup.19, 1986,
57–106) to study subfactors having finite Jones' index. Then we show that for pairs of finite …

… basis. In this article, when we do not use the adjectives left or right, by a basis we shall
always mean a right Pimsner–Popa basis (and not a two-sided basis). …

… Using the "orthonormal basis" of [3] it is easy to see that the map (p:My —► M that sends Y^…
basis of M over TV. Indeed if x' = J2, m^i EN' DM, with ni EN, then 0o(x') 6 My implies 0o(x') = …

Let A and B0 be separable C*-algebras with B0 stable and containing a full projection. Let X
be a compact, finite-dimensional topological space. We show that if τ̂ : A → 𝓜(C(X) ⊗ B0) …

… To compute Λ, we have used Pimsner-Popa orthonormal basis as the main technical tool. …
, in this article by a basis for M/N we mean a right Pimsner-Popa orthonormal basis for M/N …

… If [M:N] < oo then let {^i}i^i^n+i be as in 1.3 an "orthonormal basis" of M over N. We claim
that {wji^^.n is also a basis of M" as a module over N". Indeed, since ENG)((X^)J=(EN(X^ it …

… We remark that Pimsner-Popa bases of the form in Corollary 3.3 were recently shown in [6]
to produce unbiased teleportation schemes for tripartite quantum systems (in the commuting …

… a quasibasis for a conditional expectation, a generalization of the Pimsner-Popa basis in the
… With a quasi-basis, Watatani successfully introduced a CÃ-version of basic construction [42]…

… always admits a two-sided Pimsner-Popa basis. This is preceded by a pragmatic revisit of
… systematically study these objects and their generalities in the spirit of Pimsner-Popa basis. …