A Note on the Pettis Integral and the Bourgain Property

• 발행기관: 충청수학회
• 저자명: JONG SUL LIM GWANG SIK EUN JU HAN YOON
• 간행물 정보: 『Journal of the Chungcheong Mathematical Society』Volume 5, No. 1, 159~165쪽, 전체 7쪽
• 주제분류: 자연과학 > 자연과학일반
• 파일형태: PDF
• 발행일자: 1992.06.30

영문 초록

In 1986, R. Huff [3] showed that a Dunford integrable function is Pettis integrable if and only if T : x* →L₁ (μ) is weakly compact operator and {T(K(F,e)) I F ⊂ X, F: finite and ε > 0} = {0}. In this paper, we introduce the notion of Bourgain property of real valued functions formulated by J. Bourgain [2]. We show that the class of pettis integrable functions is linear space and if fis bounded function with Bourgain property, then T: x** → L₁(μ) by T(x**) = x** f is weak* - to - weak linear operator. Also, if operator T : L₁ (μ) → x* with Bourgain property, then we show that f is Pettis representable.

목차

ABSTRACT

I. Introduction

II. Pettis integral

III. Pettis representable

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