Duality for Lipschitz p-summing operators

By J. A. Chávez-Domínguez. 2011

47 citations recorded by the source corpus.

Abstract Building upon the ideas of R. Arens and J. Eells (1956) [1] we introduce the concept of spaces of Banach-space-valued molecules, whose duals can be naturally identified with spaces of operators between a metric space and a Banach space. On these spaces we define analogues of the tensor norms of Chevet (1969) [3] and Saphar (1970) [14] , whose duals are spaces of Lipschitz p-summing operators. In particular, we identify the dual of the space of Lipschitz p-summing operators from a finite metric space to a Banach space — answering a question of J. Farmer and W.B. Johnson (2009) [6] — and use it to give a new characterization of the non-linear concept of Lipschitz p-summing operator between metric spaces in terms of linear operators between certain Banach spaces. More generally, we define analogues of the norms of J.T. Lapreste (1976) [11] , whose duals are analogues of A. Pietschʼs ( p , r , s ) -summing operators (A. Pietsch, 1980 [12] ). As a special case, we get a Lipschitz version of ( q , p ) -dominated operators.

Subfields: Applied Mathematics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/d4a64797f7f41048068ea25f854565703f953611

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In Applied Mathematics

1. M. Villegas-Vallecillos
2. A. Jiménez-Vargas
3. Juan Matías Sepulcre

In Mathematical Physics

1. M. Villegas-Vallecillos
2. A. Jiménez-Vargas
3. Juan Matías Sepulcre

In Statistics and Probability

1. M. Villegas-Vallecillos
2. A. Jiménez-Vargas
3. Juan Matías Sepulcre

Citations in the corpus

• Lipschitz compact operators (2014, methodology): “Chávez-Domı́nguez introduced and investigated Lipschitz (p, r, s)-summing operators and Lipschitz (q, p)-mixing operators in [2] and [3], respectively.”