It will be shown that for 1 < p < 2 the Schatten p-class is isometrically isomor-phic to a subspace of the predual of a von Neumann algebra. Similar results hold for non-commutative L p (N;)-spaces deened by a semi-nite, normal, faithful trace on a von Neumann algebra N. The embeddings rely on a suitable notion of p-stable processes in the non-commutative setting.

We give a structure theorem for a ring homomorphism of a commutative regular Banach algebra into another commutative Banach algebra. In particular, it is shown that: (i) A ring homomorphism of a commutative C∗-algebra onto another commutative C∗-algebra with connected infinite Gelfand space is either linear or anti-linear. (ii) A ring automorphism of L1(R ) is either linear or anti-linear. (iii...

In this paper, we introduce the notion of hyper pseudo B C K - algebras, which is a generalization of pseudo BCK -algebras and hyper BCK -algebras and we investigates some related properties. In follow, we de ne some kinds of hyper pseudo BCK -ideals of a hyper pseudo BCK - algebra and we find the relations among them. Finally, we characterize the hyper pseudo BCK -ideals of type 4 generated by...

Given an integral commutative residuated lattices L=(L,∨,∧), its full twist-product (L2,⊔,⊓) can be endowed with two binary operations ⊙ and ⇒ introduced formerly by M. Busaniche R. Cignoli as well C. Tsinakis A. Wille such that it becomes a lattice. For every a∈L we define certain subset Pa(L) of L2. We characterize when is sublattice the (L2,⊔,⊓). In this case together some natural antitone i...

This note is devoted to the study of geometric properties and the relationships between a projective space and an exponential class, both naturally associated with the positive elements in a commutative Banach algebra. Even though the motivating problem consists of understanding the geometry of the class of densities with respect to a given measure, the formulation can be carried out in general...

1. I. S. Cohen, Commutative rings with restricted minimum conditions, Duke Math. J. 17 (1950), 27-41. 2. S. MacLane and O. F. G. Schilling, Infinite number fields with Noether ideal theories, Amer. J. Math. 61 (1939), 771-782. 3. N. Nakano, Idealtheorie in einem speziellen unendlichen algebraischen Zahlkorper, J. Sei. Hiroshima Univ. 16(1953), 425-439. 4. O. Zariski and P. Samuel, Commutative a...

For a given variety Var of algebras we define the variety Var of dialgebras. This construction turns to be closely related with varieties of pseudo-algebras: every Var-dialgebra can be embedded into an appropriate pseudo-algebra of the variety Var. In particular, Leibniz algebras are exactly Lie dialgebras, and every Leibniz algebra can be embedded into current Lie conformal algebra.