Robustness of weighted L p ?depth and L p ?median

Robustness of weighted L p - depth and L p - median

Lp-norm weighted depth functions are introduced and the local and global robustness of these weighted Lp-depth functions and their induced multivariate medians are investigated via influence function and finite sample breakdown point. To study the global robustness of depth functions, a notion of finite sample breakdown point is introduced. The weighted Lp-depth functions turn out to have the s...

operators on L ( L p ) and ` p - strictly singular operators

A classification of weakly compact multiplication operators on L(Lp), 1 < p < ∞, is given. This answers a question raised by Saksman and Tylli in 1992. The classification involves the concept of `p-strictly singular operators, and we also investigate the structure of general `p-strictly singular operators on Lp . The main result is that if an operator T on Lp , 1 < p < 2, is `p-strictly singula...

On the Robustness of the Cepheids' P-l Relation

l P

A Note on Weighted Composition Operators on L^p-Spaces