Orlicz-Pettis Theorems for Multiplier Convergent Series

Orlicz - Pettis Theorems for Multiplier Convergent Operator Valued Series

Let X,Y be locally convex spaces and L(X,Y ) the space of continuous linear operators from X into Y . We consider 2 types of multiplier convergent theorems for a series P Tk in L(X,Y ). First, if λ is a scalar sequence space, we say that the series P Tk is λ multiplier convergent for a locally convex topology τ on L(X,Y ) if the series P tkTk is τ convergent for every t = {tk} ∈ λ. We establish...

0 Orlicz - Pettis Polynomials on Banach Spaces

We introduce the class of Orlicz-Pettis polynomials between Banach spaces, defined by their action on weakly unconditionally Cauchy series. We give a number of equivalent definitions, examples and counterexamples which highlight the differences between these polynomials and the corresponding linear operators.

A bilinear version of Orlicz-Pettis theorem

Given three Banach spaces X, Y and Z and a bounded bilinear map B : X×Y → Z, a sequence x = (xn)n ⊆ X is called B-absolutely summable if ∑∞ n=1 ‖B(xn, y)‖Z < ∞ for any y ∈ Y . Connections of this space with `weak(X) are presented. A sequence x = (xn)n ⊆ X is called B-unconditionally summable if ∑∞ n=1 |〈B(xn, y), z∗〉| < ∞ Preprint submitted to Elsevier 21 December 2007 for any y ∈ Y and z∗ ∈ Z∗...

Convergence Theorems for Set-valued Denjoy-pettis Integrable Mappings

In this paper, we introduce the Denjoy-Pettis integral of set-valued mappings and investigate some properties of the set-valued Denjoy-Pettis integral. Finally we obtain the Dominated Convergence Theorem and Monotone Convergence Theorem for set-valued DenjoyPettis integrable mappings.

Stability theorems for semi{groups via Multiplier theorems