Classes of operators on vector valued integration spaces

Journal of the Australian Mathematical Society

R. J. Fleming¹ 

[1] J. E. Jamison

关键词: primary 46 E 40;    46 E 30;    47 B 99;   

DOI  :  10.1017/S1446788700020152

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

Let Lp(Ω, K) denote the Banach space of weakly measurable functions F defined on a finite measure space and taking values in a separable Hilbert space K for which ∥ F ∥p = ( ∫ | F(ω) |p)1/p < + ∞. The bounded Hermitian operators on Lp(Ω, K) (in the sense of Lumer) are shown to be of the form , where B(ω) is a uniformly bounded Hermitian operator valued function on K. This extends the result known for classical Lp spaces. Further, this characterization is utilized to obtain a new proof of Cambern's theorem describing the surjective isometries of Lp(Ω, K). In addition, it is shown that every adjoint abelian operator on Lp(Ω, K) is scalar.

【 授权许可】

Unknown