Compact bilinear operators on asymmetric normed spaces. (English) Zbl 1489.46052
This article introduces the new class of the compact bilinear mappings between asymmetric normed spaces. The author presents the basic properties, together with some fundamental theorems. He proves a Schauder type theorem on the compactness of the adjoint of a compact bilinear operator and studies the ideal properties of spaces of compact bilinear operators and an Alaoglu-Bourbaki type theorem.
Reviewer: Elhadj Dahia (Bou Saâda)
MSC:
| 46G25 | (Spaces of) multilinear mappings, polynomials |
| 47B07 | Linear operators defined by compactness properties |
| 47H60 | Multilinear and polynomial operators |
| 46B50 | Compactness in Banach (or normed) spaces |
| 54E35 | Metric spaces, metrizability |
Keywords:
asymmetric normed space; quasi-metric space; bilinear operator; bilinear form; adjoint of bilinear operator; compact operator; Schauder-type theoremReferences:
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