We show that the class of unital C-algebras is an elementary class in the language of operator systems. As a result, we have that there is a definable predicate in the language of operator systems that defines the multiplication in any C-algebra. Moreover, we prove that the aforementioned class is ∀∃∀-axiomatizable but not ∀∃-axiomatizable nor ∃∀-axiomatizable. Recall that a C∗-algebra is a ∗-s...

In this paper, we derive a generalized multiplicative Hardy-LittlewoodPolya type inequality, as well as several related additive inequalities, for functions of operators in Hilbert spaces. In addition, we find the modulus of continuity of a function of an operator on a class of elements defined with the help of another function of the operator. We then apply the results to solve the following p...

‎making use of a linear operator‎, ‎which is defined here by means of‎ ‎the hadamard product (or convolution)‎, ‎we define a subclass‎ ‎$mathcal {t}_{p}(a‎, ‎c‎, ‎gamma‎, ‎lambda; h)$ of meromorphically‎ ‎multivalent functions‎. ‎the main object of this paper is to‎ ‎investigate some important properties for the class‎. ‎we also derive‎ ‎many results for the hadamard roducts of functions belong...