Abraham Plessner attended secondary school (1909-1918) where up until 1916 he was taught in Russian, then for one year in German, then for his last year in Polish. In 1919 he entered the University of Giessen and studied under Schlesinger and Engel.
In 1921 Plessner went to Göttingen where he took courses on Dirichlet series and Galois theory by Edmund Landau; algebraic number fields by Emmy Noether; and calculus of variations by Courant. Then in session 1921/22 he studied in Berlin where von Mises lectured on differential and integral equations, Bieberbach on differential geometry and Schur on algebra.
Plessner obtained his doctorate from Giessen in 1922 for a thesis on conjugate trigonometrical series. Then he worked in Marburg with Hensel editing Kronecker's collected works. During his time in Marburg he published a paper containing what is today called Plessner's theorem, concerning the boundary behaviour of functions meromorphic in the unit disk.
In 1929 Plessner's Habilitationsschrift was submitted to the faculty at Giessen. Although it was an outstanding piece of work the Senate refused to give its approval since Plessner was a Russian citizen. He was told by the city officials that he was required to have 20 years continuous residence in Germany to obtain citizenship.
Plessner moved to Berlin and the Senate of Giessen was again requested to confer the degree. They decided to postpone a decision indefinitely and so Plessner had no choice, he could not get a lectureship in Germany since he was a Russian citizen so he moved to Moscow.
There he joined the research group of Luzin. His interests at this time moved to functional analysis and particularly spectral theory. It seems that his interest in functional analysis arose when he read Banach's book of 1932.
He was greatly respected in Moscow: a colleague wrote
Abrahm Ezechiel Plessner knew so much that it seemed he knew everything. He understood works in any field and every young mathematician tried to tell him of his new results.
His students noted that his lectures were filled with comments like: this is false and this is trivial. They jokingly wrote:-
Paradise in the sense of Plessner is an abstract space in which all theorems are both false and trivial.
Plessner was promoted to professor in 1939 and held posts both at Moscow University and at the Mathematical Institute of the USSR Academy of Sciences. However he was dismissed from both posts in 1949.
His last years were ones of financial hardship and his health, which had never been good, became steadily worse. His role in mathematics is however a major one and must be considered as a founder of the Moscow school of functional analysis.
Article by: J J O'Connor and E F Robertson