Titlebook: Biorthogonal Systems in Banach Spaces; Petr Hájek,Vicente Montesinos Santalucía,Václav Zi Textbook 2008 Springer-Verlag New York 2008 Bana

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https://doi.org/10.1007/978-0-387-68915-9Banach Space; banach spaces; functional analysis

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https://doi.org/10.1007/978-3-658-13124-1ble setting, related to this structure. When searching for a system of coordinates to represent any vector of a (separable) Banach space, a natural approach is to consider the concept of a Schauder basis. Unfortunately, not every separable Banach space has such a basis, as was proved by Enflo in [En

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https://doi.org/10.1007/978-3-658-13124-1es on some fundamental results concerning Mackey and weak topologies. For example, the first section presents some of Grothendieck’s basic results on the dual Mackey topology on dual Banach spaces. The second section includes work of Odell, Rosenthal, Emmanuele, Valdivia, and others on the sequentia

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Bank- und Kundenloyalit?t im Wandelon of long Schauder bases; the first section introduces this notion, which is a natural generalization of the usual Schauder basis. The first section also contains Plichko’s improvement of the natural “exhaustion” argument that yields the existence of a bounded total biorthogonal system in every Ban

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Exkurs: Die Erfolgsgeschichte von PING AN identity, the separable complementation property, and projectional generators. Renorming theory also plays an important role here, as spaces with an M-basis admit an equivalent rotund norm, while spaces with a strong M-basis even have an LUR renorming thanks to the fundamental result of Troyanski..