Similarities and differences between real and complex Banach spaces: an overview and recent developments

Autor:	Moslehian, M. S., Muñoz-Fernández, G. A., Peralta, A. M., Seoane-Sepúlveda, J. B.
Rok vydání:	2021
Předmět:	Mathematics - Functional Analysis Mathematics - Operator Algebras
Druh dokumentu:	Working Paper
Popis:	There are numerous cases of discrepancies between results obtained in the setting of real Banach spaces and those obtained in the complex context. This article is a modern exposition of the subtle differences between key results and theories for complex and real Banach spaces and the corresponding linear operators between them. We deeply discuss some aspects of the complexification of real Banach spaces and give several examples showing how drastically different can be the behavior of real Banach spaces versus their complex counterparts. Comment: In this second version we added some new materials and some new proofs for well-known results, 106 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2107.03740 Zobrazit plný text záznamu View this record from Arxiv