LetX and Y be vector spaces over the same field K. Following the terminology of Richard Arens [Pacific J. Math. 11 (1961), 9–23], a relation F of X into Y is called linear if λF (x) ⊂ F (λx) and F (x) + F (y) ⊂ F (x+ y) for all λ ∈ K \ {0} and x, y ∈ X. After improving and supplementing some former results on linear relations, we show that a relation Φ of a linearly independent subset E of X in...

In this paper, a new coincidence index is presented for countably P-concentrative pairs. 1. INTRODUCTION Let X and Y be metric spaces. A continuous single valued map p : Y-* X is called a Vietoris map [1,2] if the following two conditions are satisfied: (i) for each x E X, the set p-l(x) is acyclic, (ii) p is a proper map, i.e., for every compact A C X we have that p-l(A) is compact. Let D(X, Y...

We consider some second order quasilinear partial differential inequalities for real valued functions on the unit ball and find conditions under which there is a lower bound for the supremum of nonnegative solutions that do not vanish at the origin. As a consequence, for complex valued functions f(z) satisfying ∂f/∂z̄ = |f |α, 0 < α < 1, and f(0) = 0, there is also a lower bound for sup |f | on ...

This is a short comment on “The impacts of land plant evolution Earth's climate and oxygenation state – An interdisciplinary review” by Tais W. Dahl Susanne K.M. Arens, Chem. Geol. 547 (2020) Article 119665. We discuss what the sedimentary-stratigraphic record (SSR) can reveal about influence ancient plants erosion, demonstrate that intensive properties SSR are supportive hypotheses vegetation ...

Let L be a completely valued nonarchimedean field and g a finite dimensional Lie algebra over L. We show that its hyperenveloping algebra F(g) agrees with its Arens-Michael envelope and, furthermore, is a stably flat completion of its universal enveloping algebra. As an application, we prove that the Taylor relative cohomology for the locally convex algebra F(g) is naturally isomorphic to the L...

We establish a lower estimate for the Kobayashi-Royden infinitesimal pseudometric on an almost complex manifold (M, J) admitting a bounded strictly plurisubharmonic function. We apply this result to study the boundary behaviour of the metric on a strictly pseudoconvex domain in M and to give a sufficient condition for the complete hyperbolicity of a domain in (M, J). Finally we obtain the regul...

A Banach lattice algebra is a Banach lattice, an associative algebra with a sub-multiplicative norm and the product of positive elements should be positive. In this note we study the Arens regularity and cohomological properties of Banach lattice algebras.

let $a$ be a $c^*$-algebra and $e$ be a left hilbert $a$-module. in this paper we define a product on $e$ that making it into a banach algebra and show that under the certain conditions $e$  is arens regular. we also study the relationship between derivations of $a$ and $e$.