Albert algebras and other Jordan algebras are constructed over curves of genus zero and one, using a generalization of the Tits process and the first Tits construction due to Achhammer.

The Lower Jordan River is located in the semiarid area of the Jordan Valley, along the border between Israel and Jordan. The implementation of the water sections of the peace treaty between Israel and Jordan and the countries' commitment to improve the ecological sustainability of the river system require a better understanding of the riverine environment. This paper investigates the sources an...

Let B(X ) be the algebra of all bounded linear operators on a complex Banach space X and let I(X ) be the set of non-zero idempotent operators in B(X ). A surjective map φ : B(X ) → B(X ) preserves nonzero idempotency of the Jordan products of two operators if for every pair A, B ∈ B(X ), the relation AB + BA ∈ I(X ) implies φ(A)φ(B) + φ(B)φ(A) ∈ I(X ). In this paper, the structures of linear s...

We present an efficient algorithm for obtaining a canonical system of Jordan chains for an n×n regular analytic matrix function A(λ) that is singular at the origin. For any analytic vector function b(λ), we show that each term in the Laurent expansion of A(λ)−1b(λ) may be obtained from the previous terms by solving an (n+d)× (n+d) linear system, where d is the order of the zero of detA(λ) at λ ...

In 1996, Harris and Kadison posed the following problem: show that a linear bijection between C∗-algebras that preserves the identity and the set of invertible elements is a Jordan isomorphism. In this paper, we show that if A and B are semisimple Banach algebras andΦ : A→ B is a linear map onto B that preserves the spectrum of elements, thenΦ is a Jordan isomorphism if either A or B is a C∗-al...

Let B(X ) be the algebra of all bounded linear operators on a complex Banach space X and let I(X ) be the set of non-zero idempotent operators in B(X ). A surjective map φ : B(X ) → B(X ) preserves nonzero idempotency of the Jordan products of two operators if for every pair A, B ∈ B(X ), the relation AB +BA ∈ I(X ) implies φ(A)φ(B)+φ(B)φ(A) ∈ I(X ). In this paper, the structures of linear surj...

Let A,B be two unital C∗−algebras. We prove that every almost unital almost linear mapping h : A −→ B which satisfies h(3uy + 3yu) = h(3u)h(y) + h(y)h(3u) for all u ∈ U(A), all y ∈ A, and all n = 0, 1, 2, ..., is a Jordan homomorphism. Also, for a unital C∗−algebra A of real rank zero, every almost unital almost linear continuous mapping h : A −→ B is a Jordan homomorphism when h(3uy + 3yu) = h...