WHEN we speak of a 'back and forth' construction for proving the isomorphism of two countable structures we call to mind the famous theorem of Cantor that any countable dense linearly ordered set without end-points is order-isomorphic to Q. Cantor's own proof requires only the 'going forth' part of the construction, however, and Adrian Mathias, on noticing this, asked for a classification of th...

The purpose of this paper is to establish a connection between semisimple Jordan algebras and certain invariant differential operators on symmetric spaces; and to prove an identity for such operators which generalizes the classical Capelli identity. The norm function on a simple real Jordan algebra gives rise to invariant differential operators Dm on a certain symmetric space which is a natural...

Let M and N be complex unital Jordan-Banach algebras, let M−1 N−1 denote the sets of invertible elements in N, respectively. Suppose that M⊆M−1 N⊆N−1 are clopen subsets N−1, respectively, which closed for powers, inverses products form Ua(b). In this paper we prove each surjective isometry Δ:M→N there exists a real-linear T0:M→N an element u0 McCrimmon radical such Δ(a)=T0(a)+u0 all a∈M. Assumi...

We study the ground-state properties of hard-core bosons trapped by arbitrary confining potentials on one-dimensional optical lattices. A recently developed exact approach based on the Jordan-Wigner transformation is used. We analyze the large distance behavior of the one-particle density matrix, the momentum distribution function, and the lowest natural orbitals. In addition, the low-density l...

In this paper, we give a characterization of strongly Jordan zero-product preserving maps on normed algebras as a generalization of  Jordan zero-product preserving maps. In this direction, we give some illustrative examples to show that the notions of strongly zero-product preserving maps and strongly Jordan zero-product preserving maps are completely different. Also, we prove that the direct p...

In this paper, we introduce n-jordan homomorphisms and n-jordan *-homomorphisms and Also investigate the Hyers-Ulam-Rassiasstability of n-jordan *-homomorphisms on C*-algebras.

Participants pressed computer keys to keep a moving dot stimulus within a rectangle, either alone or with a partner they could neither see nor hear. Pressing the A-key or L-key caused the dot to move right or left, respectively, for as long as the key was pressed. Switching between the A and L keys (i.e., turning) proved challenging: concurrently pressing both keys made the stimulus move upward...

We prove variants of Wiener's Tauberian theorem in the framework quantum harmonic analysis, i.e. for convolutions between an absolutely integrable function and a trace class operator, or two operators. Our results include as special case. Applications our theorems are related to localization operators, Toeplitz isomorphism Bargmann-Fock spaces quantization schemes with consequences Shubin's pse...

in this paper, we introduce n-jordan homomorphisms and n-jordan *-homomorphisms and also investigate the hyers-ulam-rassiasstability of n-jordan *-homomorphisms on c*-algebras.