BANACH, Stefan. Première édition de la Théorie des Opérations Linéaires. 1932

Titre : Théorie des Opérations Linéaires.

Éditeur : Zu Subwencji Funduszu Kultury Narodowej, Warsaw

Date d'édition : 1932

Edition : First edition

 

Théorie des Opérations Linéaires.

BANACH, Stefan.

Description :

The copy of Andrew M. Gleason . "With the appearance in 1932 of [von Neumann's] 'Mathematische Grundlagen der Quantenmechanik' and Banach's 'Théorie des opérations linéaires', functional analysis was established as one of the most important fields of modern analysis, as an independent mathematical discipline." (Grattan-Guiness: Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences, p.384). "From 1922 on, Banach introduced through his papers the concept of normed linear spaces and investigated them (and metric linear spaces), particularly regarding the assumption of completeness (complete normed linear spaces are now generally known as Banach spaces). The concept was introduced at almost the same time by Norbert Wiener (who about a quarter of a century later founded cybernetics), but he did not develop the theory, perhaps because he did not see its possible application. Banach proved three fundamental theorems of the theory of normed linear spaces: the theorem on the extension of continuous linear functionals, now called Hahn-Banach theorem (they proved it independently, and Hahn actually did so first); the theorem on bounded families of mappings, now called the Banach-Steinhaus theorem; and the theorem on continuous linear spaces. He also introduced and examined the concept of weak convergence and weak closure, and gave a series of applications of the general theorems on normed linear spaces. . The theory of these spaces is an indispensable tool and the basis of contemporary theory of more general linear spaces; it also provided the stimulus and the staring point for other branches of functional analysis." (DSB: I, p.428). The Honeyman Collection, Part I, lot 194. Published as the first volume of the series 'Monografje Matematcyzne Seminar Mat. Uivw. Warsz I, Warsaw, druk M. Garasinski'. 8vo: 252 x 156 mm. Original printed wrappers; corners a little bumped, and spine slightly sunned. In all a very good copy. VII,(1),254, (2:adverts) pp. . N° de réf. du libraire 2520

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