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On Lipschitz \(\tau ( p) \)-summing operators. (English) Zbl 1384.46014
The notion of \(\tau\)-summing linear operators was introduced by A. Pietsch [Operator ideals. Amsterdam etc.: North-Holland (1980; Zbl 0434.47030)] and X. Mujica [Port. Math. (N.S.) 65, No. 2, 211–226 (2008; Zbl 1152.46035)] extended this to multilinear operators. In the paper under review, the authors generalize this class to Lipschitz operators. Some properties are provided and, by using a technique from D. Pellegrino et al. [Adv. Math. 229, No. 2, 1235–1265 (2012; Zbl 1248.47024); Bull. Lond. Math. Soc. 44, No. 6, 1292–1302 (2012; Zbl 1269.47020)], a characterization of the Lipschitz operators is presented introduced via a domination theorem. The authors generalize the class of Cohen \(p\)-nuclear operators to Lipschitz operators and also investigate the relationships between various classes of Lipschitz operators.

MSC:
46B28 Spaces of operators; tensor products; approximation properties
47L20 Operator ideals
46T99 Nonlinear functional analysis
47H99 Nonlinear operators and their properties
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