@article{cfd82662cee94655907c04ba47312ac4,

title = "Norming subspaces of banach spaces",

abstract = "We show that if X is a closed subspace of a Banach space E and Z is a closed subspace of E* such that Z is norming for X and X is total over Z (as well as X is norming for Z and Z is total over X), then X and the preannihilator of Z are complemented in E whenever Z is w*-closed or X is reflexive.",

keywords = "M-bibasic system, Norming subspace, Reflexive subspace, Total subspace",

author = "Fonf, {V. P.} and S. Lajara and S. Troyanski and C. Zanco",

note = "Funding Information: The first and fourth authors were partially supported by the Gruppo Nazionale per l{\textquoteright}Analisi Matematica, la Probabilit{\`a} e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM) of Italy. Funding Information: The third author was supported by MICINN project MTM2014-54182-P (Spain), by MTM2017-86182-P (AEI/FEDER, UE), by the Fundaci{\'o}n S{\'e}neca (Agencia de Ciencia y Tec-nolog{\'i}a de la Regi{\'o}n de Murcia) under project 19275/PI/14 and by the Bulgarian National Scientific Fund. DFNI-I02/10, 2015. Funding Information: The first and fourth authors were partially supported by the Gruppo Nazionale per l?Analisi Matematica, la Probabilit? e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM) of Italy. The second author was supported by MICINN projects MTM2014-54182-P and MTM2015-65825-P (Spain), by MTM2017-86182-P (AEI/FEDER, UE) and by the Fundaci?n S?neca (Agencia de Ciencia y Tecnolog?a de la Regi?n de Murcia) under project 19275/PI/14. The third author was supported by MICINN project MTM2014-54182-P (Spain), by MTM2017-86182-P (AEI/FEDER, UE), by the Fundaci?n S?neca (Agencia de Ciencia y Tecnolog?a de la Regi?n de Murcia) under project 19275/PI/14 and by the Bulgarian National Scientific Fund. DFNI-I02/10, 2015. Funding Information: The second author was supported by MICINN projects MTM2014-54182-P and MTM2015-65825-P (Spain), by MTM2017-86182-P (AEI/FEDER, UE) and by the Fundaci{\'o}n S{\'e}neca (Agen-cia de Ciencia y Tecnolog{\'i}a de la Regi{\'o}n de Murcia) under project 19275/PI/14. Publisher Copyright: {\textcopyright} 2019 American Mathematical Society.",

year = "2019",

month = jan,

day = "1",

doi = "10.1090/proc/14442",

language = "English",

volume = "147",

pages = "3039--3045",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "7",

}