We introduce a new class of bi-univalent functions defined in the open unit disc and connected with a -convolution. We find estimates for the general Taylor-Maclaurin coefficients of the functions in this class by using Faber polynomial expansions and we obtain an estimation for the Fekete-Szegö problem for this class.
In this paper we show that a Rosenthal operator factors through a Banach space containing no isomorphs of l1.
It is proved that every positive Banach-Saks operator T: E → F between Banach lattices E and F factors through a Banach lattice with the Banach-Saks property, provided that F has order continuous norm. By means of an example we show that this order continuity condition cannot be removed. In addition, some domination results, in the Dodds-Fremlin sense, are obtained for the class of Banach-Saks operators.
We study the following problem: Given a homogeneous polynomial from a sublattice of a Banach lattice to a Banach lattice, under which additional hypotheses does this polynomial factorize through -spaces involving multiplication operators? We prove that under some lattice convexity and concavity hypotheses, for polynomials certain vector-valued norm inequalities and weighted norm inequalities are equivalent. We combine these results and prove a factorization theorem for positive homogeneous polynomials...
Consider the following conditions. (a) Every regular LB-space is complete; (b) if an operator T between complete LB-spaces maps bounded sets into relatively compact sets, then T factorizes through a Montel LB-space; (c) for every complete LB-space E the space C (βℕ, E) is bornological. We show that (a) ⇒ (b) ⇒ (c). Moreover, we show that if E is Montel, then (c) holds. An example of an LB-space E with a strictly increasing transfinite sequence of its Mackey derivatives is given.