Abstract Every finite subunital of any generalized hermitian unital is itself a unital; the embedding given by an quadratic field extensions. In particular, with one (i.e., it originates from separable extension).

In this paper we prove that every n-Jordan homomorphis varphi:mathcal {A} longrightarrowmathcal {B} from unital Banach algebras mathcal {A} into varphi -commutative Banach algebra mathcal {B} satisfiying the condition varphi (x^2)=0 Longrightarrow varphi (x)=0, xin mathcal {A}, is an n-homomorphism. In this paper we prove that every n-Jordan homomorphism varphi:mathcal {A} longrightarrowmathcal...

We show that standard deviation σ satisfies the Leibniz inequality σ(fg) ≤ σ(f)‖g‖ + ‖f‖σ(g) for bounded functions f, g on a probability space, where the norm is the supremum norm. A related inequality that we refer to as “strong” is also shown to hold. We show that these in fact hold also for noncommutative probability spaces. We extend this to the case of matricial seminorms on a unital C*-al...

LetX be a compact metric space and let Λ be a Z (k ≥ 1) action onX.We give a solution to a version of Voiculescu’s problem of AF-embedding: The crossed product C(X) ⋊Λ Z k can be embedded into a unital simple AF-algebra if and only if X admits a strictly positive Λ-invariant Borel probability measure. Let C be a unital AH-algebra, let G be a finitely generated abelian group and let Λ : G → Aut(...

We consider unital simple inductive limits of generalized dimension drop C∗-algebras They are so-called ASH-algebras and include all unital simple AH-algebras and all dimension drop C∗-algebras. Suppose that A is one of these C∗-algebras. We show that A ⊗ Q has tracial rank no more than one, where Q is the rational UHF-algebra. As a consequence, we obtain the following classification result: Le...

Let A be a unital algebra and M be a unital A-bimodule. A characterization of generalized derivations and generalized Jordan derivations from A into M, through zero products or zero Jordan products, is given. Suppose that M is a unital left A-module. It is investigated when a linear mapping from A into M is a Jordan left derivation under certain conditions. It is also studied whether an algebra...

Suppose that A and B are unital Banach algebras with units 1A and 1B , respectively, M is a unital Banach A−B-bimodule, T =   A M 0 B   is the triangular Banach algebra, X is a unital T -bimodule, XAA = 1AX1A, XBB = 1BX1B , XAB = 1AX1B and XBA = 1BX1A. Applying two nice long exact sequences related to A, B, T , X, XAA, XBB , XAB and XBA we establish some results on (co)homology of triangu...

We present a new construction of non-classical unitals from a classical unital U in PG(2, q2). The resulting non-classical unitals are B-M unitals. The idea is to find a non-standard model Π of PG(2, q2) with the following three properties: (i) points of Π are those of PG(2, q2); (ii) lines of Π are certain lines and conics of PG(2, q2); (iii) the points in U form a non-classical B-M unital in ...

We identify the points of PG(2, q) with the directions of lines in GF(q3), viewed as a 3dimensional affine space over GF(q). Within this framework we associate to a unital in PG(2, q) a certain polynomial in two variables, and show that the combinatorial properties of the unital force certain restrictions on the coefficients of this polynomial. In particular, if q = p2 where p is prime then we ...

An l-group G is an abelian group equipped with a translation invariant lattice order. Baker and Beynon proved that G is finitely generated projective iff it is finitely presented. A unital l-group is an l-group G with a distinguished order unit, i.e., an element 0 ≤ u ∈ G whose positive integer multiples eventually dominate every element of G. While every finitely generated projective unital l-...