For the Fr'{e}chet algebras $(A, (p_k))$ and $(B, (q_k))$ and $n in mathbb{N}$, $ngeq 2$, a linear map $T:A rightarrow B$ is called textit{almost $n$-multiplicative}, with respect to $(p_k)$ and $(q_k)$, if there exists $varepsilongeq 0$ such that$$q_k(Ta_1a_2cdots a_n-Ta_1Ta_2cdots Ta_n)leq varepsilon p_k(a_1) p_k(a_2)cdots p_k(a_n),$$for each $kin mathbb{N}$ and $a_1, a_2, ldots, a_nin A$. Th...

we consider the space of weakly almost periodic functions on a transformation semigroup (s, x , ?) and show that if x is a locally compact noncompact uniform space, and ? is a separately continuous, separately proper, and equicontinuous action of s on x, then every continuous function on x, vanishing at infinity is weakly almost periodic. we also use a number of diverse examples to show that th...

We investigate some subtle and interesting phenomena in the du-ality theory of operator spaces and operator algebras. In particular, we give several applications of operator space theory, based on the surprising fact that certain maps are always w *-continuous on dual operator spaces. For example, this yields a new characterization of the σ-weakly closed (possibly nonunital and nonselfadjoint) ...

Motivated by the equivalent definition of a continuous operator between Banach spaces in terms weakly null nets, we introduce unbounded operators replacing weak convergence with absolutely (uaw-convergence) lattices. We characterize order lattices and reflexive these operators. Moreover, motivated characterizing lattice Cauchy sequences, consider pre-unbounded which maps uaw-Cauchy sequences to...

where 0 c R* is a bounded open set, u: R --* W, and Vtklu denotes the set of all partial derivatives nf of u of ail orders 11) < k. The admissible functions u are required to satisfy suitable boundary conditions or other constraints. It is well known that if I is sequentially weakly lower semicontinuous in the Sobolev space wk,“(.Q), 1 < a < co, and if F satisfies certain growth conditions, the...

‎in this paper‎, ‎we investigate some results on natural metrics on the $mu$-normal functions and meromorphic $q_p$-classes‎. ‎also‎, ‎these classes are shown to be complete metric spaces with respect to the corresponding metrics‎. ‎moreover‎, ‎compact composition operators $c_phi$ and lipschitz continuous operators acting from $mu$-normal functions to the meromorphic $q_p$-classes are characte...

in this note some useful properties of strongly continuous two-parameter semigroups of operators are studied, an exponential formula for two-parameter semigroups of operators on banach spaces is obtained and some applied examples of two-parameter dynamical systems are discussed