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Multipolynomials: an almost symmetrical approach. (English) Zbl 1481.46039

Summary: In this paper, we explore a new concept of symmetric multilinear mappings and introduce a new approach to the concept of multipolynomials. We generalize several results of homogeneous polynomials and symmetric multilinear mappings, such as the classic Polarization Formula. We also present a concept of coherence and compatibility for sequences of pairs formed by multipolynomial ideals and multi-ideals. Then, we move on to a more practical analysis, using different classes of multilinear mappings and homogeneous polynomials to check the limits of these definitions.

MSC:

46G25 (Spaces of) multilinear mappings, polynomials
47H60 Multilinear and polynomial operators
47L22 Ideals of polynomials and of multilinear mappings in operator theory
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