Bihypercyclic bilinear mappings

Karl G. Grosse-Erdmann; Sung Guen Kim

doi:10.1016/j.jmaa.2012.10.056

Bihypercyclic bilinear mappings

Karl G. Grosse-Erdmann, Sung Guen Kim

Universite de Mons

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

We propose a notion of orbit for bilinear mappings on Banach spaces. This then leads us to the concept of bihypercyclic bilinear mappings, that is, of bilinear mappings with a dense orbit. We provide some examples of such mappings, and we obtain some basic properties of bihypercyclicity. In our main result we show that every separable (real or complex) Banach space supports a bihypercyclic bilinear mapping. We also formulate some open problems.

Original language	English
Pages (from-to)	701-708
Number of pages	8
Journal	Journal of Mathematical Analysis and Applications
Volume	399
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2012.10.056
State	Published - 15 Mar 2013

Keywords

Bihypercyclic bilinear mappings
Bilinear mappings
Dense orbits

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10.1016/j.jmaa.2012.10.056

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AB - We propose a notion of orbit for bilinear mappings on Banach spaces. This then leads us to the concept of bihypercyclic bilinear mappings, that is, of bilinear mappings with a dense orbit. We provide some examples of such mappings, and we obtain some basic properties of bihypercyclicity. In our main result we show that every separable (real or complex) Banach space supports a bihypercyclic bilinear mapping. We also formulate some open problems.

KW - Bihypercyclic bilinear mappings

KW - Bilinear mappings

KW - Dense orbits

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Bihypercyclic bilinear mappings

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Keywords

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