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Technical University of Crete
Technical University of Crete
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| URI: | http://purl.tuc.gr/dl/dias/126CE0CE-F6E6-4F29-9D39-1B6846D5D900 | ||
| Year | 2025 | ||
| Type of Item | Diploma Work | ||
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| Bibliographic Citation | Charalabos Kyriakou, "Real and vector valued Martingales", Diploma Work, School of Electrical and Computer Engineering, Technical University of Crete, Chania, Greece, 2025 https://doi.org/10.26233/heallink.tuc.103057 | ||
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In this work, we study (discrete) martingales with values in a normed space We provide a different proof for a special case of a Theorem from M. Girardi and W. Johnson, Universal non Completely Continuous Operators, Israel Journal of Mathematics 99, (1997), 207-219. We prove the following theorem: If a martingale is not Cauchy in the Pettis norm, then there exists an operator such that the martingale is not Cauchy in the Pettis norm. In the language of operators, the above theorem is formulated as follows: If an operator is not Dunford-Pettis (D-P), then there exists an operator such that the operator is not D-P. Following this, we present known theorems from the theory of normed spaces concerning the Radon–Nikodym property (RNP).
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