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Abstract: This paper is devoted to the study of orthogonality and disjointness preserving linear maps between Fourier and Fourier–Stieltjes algebras of locally compact groups. We show that a linear bijection (resp. ) between two Fourier algebras (resp. Fourier–Stieltjes algebras) of locally compact groups will induce a topological group isomorphism between and , provided that Ψ preserves both disjointness and some kind of orthogonality. This improves earlier results of J.J. Font and M.S. Monfared, where amenability of the groups or continuity of the linear maps are assumed. We also study the structure of bounded and unbounded disjointness preserving linear functionals of Fourier algebras. In the development, general results about disjointness and orthogonality preserving linear maps between -algebras, -algebras and their preduals are obtained. [Copyright &y& Elsevier]

Let 1 ≤ p ≤ + ∞ . We show that the positive part of the closed unit ball of a non-commutative L p -space, as a metric space, is a complete Jordan ⁎ -invariant for the underlying von Neumann algebra. [ABSTRACT FROM AUTHOR]

In this paper, we study bijective linear maps θ : A → B between A W ⁎ -algebras preserving either zero products or range orthogonality. Such a map is automatically continuous, and provides an algebra or a ⁎-algebra isomorphism π ( ⋅ ) = θ ( ⋅ ) θ ⁎ ⁎ ( 1 ) − 1 from A onto B . Our results extend previous works for the case of W ⁎ -algebras, and also cover such maps between C ⁎ -algebras satisfying an extra assumption on preserving abelian C ⁎ -subalgebras. [ABSTRACT FROM AUTHOR]