Abstract
The concept of a dyadic representation was used for the first time in 1963, when I constructed traces of operators (acting on a Banach space) whose sequence of approximation numbers is summable. Only recently, in a series of papers, those representations played the decisive role in describing all traces on arbitrary operator ideals over the separable infinite-dimensional Hilbert space. Now this method is extended to operator ideals on Banach spaces defined by means of generalized approximation numbers. The results are demonstrated on the example of convolution operators generated by functions belonging to certain Lipschitz/Besov spaces.
Mathematics Subject Classification (2010). Primary 47B10, 35S05. Secondary 46B45.
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Pietsch, A. (2017). Traces on Operator Ideals and Related Linear Forms on Sequence Ideals (Part IV). In: Bini, D., Ehrhardt, T., Karlovich, A., Spitkovsky, I. (eds) Large Truncated Toeplitz Matrices, Toeplitz Operators, and Related Topics. Operator Theory: Advances and Applications, vol 259. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-49182-0_24
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DOI: https://doi.org/10.1007/978-3-319-49182-0_24
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-49180-6
Online ISBN: 978-3-319-49182-0
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