P. L. Chebyshev (1821–1894)

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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...

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...

Commutators on L p , 1 ≤ p < ∞ †

The operators on Lp = Lp[0, 1], 1 ≤ p < ∞, which are not commutators are those of the form λI + S where λ , 0 and S belongs to the largest ideal in L(Lp). The proof involves new structural results for operators on Lp which are of independent interest.

P. F. Bonventre and L. L. Kempe

A study was made pertaining to the variations in sensitivity to inhibitors that may be encountered in industrial deterioration problems. The results indicate that at least three types of variations are involved: first, the variation in sensitivity of different strains, secondly, the variation in sensitivity of an individual strain, and finally, the variation produced by the particular environme...