Banach Spaces and their Applications

International conference dedicated to 70th anniversary of Professor A.M.Plichko

Anatolij Mykolajovych Plichko 

(Tolya for friends) was born on July 20, 1949 in the village Chervona Kamyanka in Kirovograd Region in Central Ukraine. Outstanding mathematical abilities which Anatolij demonstrated during elementary and middle school years encouraged his parents to send him to Kyiv boarding school for physical and mathematical sciences.


After graduating from this school Anatolij was accepted to Kyiv University where he was majoring in Mathematics. His research interests started to develop when he was attending a course “Topological Vector Spaces” which Yuri Petunin was teaching using the Bourbaki’s book as a text. In this course Petunin suggested his students several research problems, solving some of them was the first experience of mathematical research for Anatolij. In 1972 Anatolij got his Master’s degree and entered a Ph. D. program. He completed his Ph. D. Thesis under supervision of Petunin in 1975.


Eventually Banach space theory became the main area of research interests for Anatolij (it was not the case for his Ph. D. advisor Petunin). In this connection Anatolij established close scientific contacts with the most authoritative Soviet expert in Banach space theory - Mikhail Kadets (whose last name is also spelled as Kadec), and members of Kadets’ school (Vladimir Fonf, Boris Godun, Vladimir Kadets, Mikhail Ostrovskii).


Anatolij shares the view on mathematics as a source of attractive problems, this view was promoted by Mikhail Kadets during all of his research career.


Anatolij was successful with very many of such problems.


Anatolij has deep interests in history and Ukrainian literature. His high ethical standards, high level of independence, ability to get interested quickly in a rather distant research direction attracted to him many colleagues and students during his research career.



  • Arrival of participants - June 25;
  • Working days - June 26-28 (plenary lectures & sections);
  • Excursion day - June 29 (history lecture, the Scottish café, center of Lviv, Lviv cemetery and the grave of Stefan Banach);
  • Departure  of participants - June 30.



  • Geometry of Banach spaces (M.Ostrovskii, A.Zagorodnyuk)
  • Operator theory (R.Hryniv, Ya.Mykytyuk)
  • Applications of Banach space theory (A.Prykarpatsky)
  • Real and Complex Analysis. (I.Chyzhykov, V.Maslyuchenko, O.Skaskiv)
  • Topology and Topological Algebra (T.Banakh, O.Gutik, M.Zarichny)
  • History of Mathematics (A.Plichko, Ya.Prytula)



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University of Lviv 

The University of Lviv is one of the oldest university foundation in Ukraine, dating from 1661 when the Polish King, John II Casimir, granted it its first royal charter. Over the centuries it underwent transformations, suspensions and name changes that reflected the geo-political complexities of this part of Europe.

Jan Kazimierz University of Lviv (1919-1939) 

Prof. Zermelo visiting Lviv University on May 25-26, 1929:

Standing (from the left): K.Kuratowski, B.Knaster, S.Banach, W.Stożek, E.Żyliński, S.Riziewicz. Seating (from the left): H.Steinhaus, E.Zermelo, S.Mazurkiewicz.

The following known mathematicians were professors of Lviv University and Polytechnical Institute or have defended their PhD theses: H.Auerbach, S.Banach, Z.Birnbaum, S.Kaczmarz, K.Kuratowski, S.Mazur, W.Niclibortz, W.Orlicz, J.Pepis, J.Schauder, H.Steinhaus, M.Zaritsky,  

S.Banach and H.Steinhaus were founded the journal Studia Mathematica in 1929, first nine issues of which have been published in Lviv.  

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The Scottish Book and Scottish Cafe

The famous Scottish book was written in Lviv at the Scottish Café. The original cafe was renovated in May 2014. Here you can find a copy of the Scottish Book and “The Lviv Scottish Book”, where you can write your mathematical problem or solve the open problem from the book.

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Ivan Franko National University in Lviv, nowadays

In 1939, after the German invasion of Poland and the accompanying Soviet invasion, the Soviet administration permitted classes to continue. Until late 1939, the school worked in the pre-war Polish system. On October 18, however, the Polish rector, Professor Roman Longchamps de Bérier was dismissed, and was replaced by a prominent Ukrainian historian, Mykhailo Marchenko, grandfather of Ukrainian journalist and dissident Valeriy Marchenko. Marchenko was determined to transform the University of Lwow into the Ukrainian National University. On January 8, 1940, the university was renamed Ivan Franko Lviv State University. Polish professors and administrative assistants were increasingly fired and replaced by Ukrainians or Russians, specializing in Marxism, Leninism, political economics, as well as Ukrainian and Soviet literature, history and geography. This was accompanied by the closing of departments seen as related with the religion, free-market economics, capitalism, or the West in general; this included Polish geography, literature, or history. Lectures were held in Ukrainian and Polish (as auxiliary). From 1939 to 1941, the Soviets also executed over a dozen members of the Polish faculty.

In July 1941 the Nazi German occupiers closed the university, followed by the massacring two dozen Polish professors (as well as members of their households and guests, increasing the total number of victims to more than forty), who included members of other academic institutions, too. A statement of many scientists that Ukrainian nationalists have been involved in identifying and selecting some of the victims has no proof; see A. Plichko TWO REMARKS ON THE BOOK BY ROMAN DUDA “PEARLS FROM A LOST CITY. THE LVOV SCHOOL OF MATHEMATICS” Mat. Stud. 2017, vol. 47 (2).

In the summer of 1944, the advancing Red Army, assisted by Polish Home Army forces locally implementing Operation Burza, pushed the Wehrmacht out of Lviv and the university reopened. At first, its academic staff consisted of Poles, but within the following months most of them, together with the Polish population of the city, were "evacuated", i.e. expelled, as Stalin had moved Poland's borders far to the west. The traditions of Jan Kazimierz University have been preserved at the University of Wrocław, which was established replacing the University of Breslau after the German inhabitants of Breslau/Wrocław had been expelled following Stalin's establishing Germany's eastern border farther to the west.

The proclamation of the independence of Ukraine in 1991 brought about radical changes in every sphere of University life. Professor, Doctor Ivan Vakarchuk, a renowned scholar in the field of Theoretical Physics, had been Rector of the University since 1990 till 2013. Meeting the requirements arising in recent years new faculties and departments have been set up: the Faculty of International Relations and the Faculty of Philosophy (1992), the Faculty of Pre-Entrance University Preparation (1997), the Chair of Translation Studies and Comparative Linguistics (1998). Since 1997 the following new units have come into existence within the teaching and research framework of the University: the Law College, The Humanities Centre, The Institute of Literature Studies, The Italian Language and Culture Resource Centre. The teaching staff of the University has increased amounting to 981, with scholarly degrees awarded to over two thirds of the entire teaching staff. There are over one hundred laboratories and working units as well as the Computing Centre functioning here. The Zoological, Geological, Mineralogical Museums together with those of Numismatics, Sphragistics and Archeology are stimulating the interests of students.

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