Journal of the Australian Mathematical Society | |
Classes of operators on vector valued integration spaces | |
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
【 预 览 】
Files | Size | Format | View |
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RO201912040542883ZK.pdf | 485KB | download |