Similarities and differences between real and complex Banach spaces: an overview and recent developments
Mohammad Sal Moslehian, Gustavo A. Muñoz-Fernández, Antonio M. Peralta, Juan B. Seoane‐Sepúlveda
2022Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas21 citationsDOIOpen Access PDF
Abstract
Abstract 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.
Topics & Concepts
Banach spaceExposition (narrative)Context (archaeology)Pure mathematicsBanach manifoldMathematicsLinear operatorsComplexificationInterpolation spaceLp spaceFunctional analysisMathematical analysisGeographyBiochemistryChemistryArchaeologyLiteratureBounded functionGeneArtAdvanced Banach Space TheoryHolomorphic and Operator TheoryAdvanced Topics in Algebra