# Andrzej Tadeusz Alexiewicz

### Quick Info

Lemberg, Galicia, Austrian Empire (now Lviv, Ukraine)

Poznań, Poland

**Andrzej Alexiewicz**was a Polish mathematician, born in what is now Ukraine, who was an expert at functional analysis.

### Biography

**Andrzej Alexiewicz**was born in Lwów at a time when the city was at the centre of battles by the forces of Austria-Hungary, who had controlled the city for many years, and Russian forces. After World War I ended in 1918, Ukrainian soldiers who had been part of the Austrian army tried to take over the city and make it part of the Ukraine. However, after Poland was again recognised as an independent country with Lwów a major Polish city, Russian armies again attacked the city in 1920. They were repelled and Lwów was recognised by the international community as part of Poland in March 1923. The city quickly became an important Polish centre for learning and culture and it was in this atmosphere that Andrzej's education took place. (Lwów is now Lviv in Ukraine.) His parents were both medical doctors and were able to give their son a good education. He attended the Sixth Classical Grammar School in Lwów, graduating in 1935 at the age of eighteen.

After graduating from High School, Alexiewicz began his studies at the Jan Kazimierz University in Lwów. It was the third largest of Poland's universities, having around 6000 students when Alexiewicz began to study there. After his first year of study, 1935-36, during which he studied mathematics and physics, he concentrated exclusively on mathematics. He was taught by world-leading mathematicians such as Herman Auerbach (1901-1942), Stefan Banach, Stefan Kaczmarz (1895-1939), Stanisław Mazur, Władysław Orlicz, Julius Schauder, Hugo Steinhaus, and Eustachy Żyliński (1889-1954). This outstanding School of Mathematics in Lwów was about to be completely devastated by World War II. For example, Auerbach was Jewish and murdered by the Nazis in 1942. Kaczmarz also died during the war. Some say he was murdered by the Russians, others say he was killed in fighting. Żyliński, however, who worked on number theory, algebra, logic and the foundations of mathematics, survived the war and taught in Gliwice from 1946 to 1951. He was supervising Alexiewicz's Master's thesis when World War II started. Żyliński had supervised Władysław Orlicz's doctoral thesis on orthogonal series and it was Orlicz who became a friend, advisor and collaborator of Alexiewicz.

At the start of World War II in 1939, Russia and Germany had a pact, the so-called Ribbentrop-Molotov pact, to divide Poland between them. The two-pronged attack - the Germans from the west and the Russians from the east - quickly defeated the Polish army and Lwów was taken over by the Soviet Union. Although it was now under Soviet control, the university attempted to continue to operate as normally as possible despite many arrests and deportations carried out by the occupiers. This was not easy for, in the period from September 1939 to June 1941, the Soviets murdered over a dozen of the Jan Kazimierz University faculty. In 1941 Alexiewicz was appointed as an assistant lecturer at the Lwów State University, but in June 1941 Germany attacked its former ally, the Soviet Union. On 1 July 1941 German troops entered Lwów and on the following day 36 professors who had worked at the university were arrested. All but one of the professors were shot by the Germans. The university could no longer operate, so Alexiewicz had to give up his position there.

After the Germans occupied Lwów they ordered Rudolf Weigl to set up a vaccine production plant at his Institute in the city. Many people worked there, including many academics, Jews, and people in the Polish underground. Alexiewicz was one of the academics working there, but he also taught in an underground university, and continued to undertake research towards his doctorate. Władysław Orlicz was his thesis advisor and in August 1944, he defended his thesis

*On sequences of operations*before a committee consisting of his supervisor, Władysław Orlicz, the dean of mathematics and science at the underground Jan Kazimierz University, August Zierhoffer (1893-1969), and the physicist, Jan Nikliborc (1902-91). In fact, several years later, Alexiewicz submitted a two-part paper

*On sequences of operations*based on his thesis to

*Studia Mathematica*which was published in volume 11 in 1949-50. It contains the following note:-

Presented, with some minor differences, as a PhD thesis on 10 March 1944 in secret to the University of Lwów, during the terror of the German occupation.Now, as the war entered its final stages, Alexiewicz realised that Lwów would not remain a part of Poland when the war ended. By this time Alexiewicz was married with children; his son Władysław Alexiewicz, who became a famous physicist, was born in November 1943. Orlicz had been appointed to a chair at Poznań University in 1937 but had been on holiday in Lwów when the war started. There had been no point in him returning to Poznań, as we explain below, so he had spent the war years in Lwów. Once the war ended, however, he could return to Poznań. This made Poznań a natural choice for Alexiewicz since he would remain a colleague of Orlicz. Together with his family, Alexiewicz arrived in Poznań on 5 May 1945. Orlicz, who held the chair of mathematics, and Alexiewicz then faced a major task rebuilding the department of mathematics at Poznań which had been completely destroyed during the war.

In fact the University of Poznań had been closed by the Germans in October 1939, and many of the faculty were arrested. In 1941 the Germans opened a new German University of Poznań, but it was not well received; it operated until 1944. The reopened Polish University of Poznań, to which Orlicz and Alexiewicz were appointed, was a small institution with hardly any infrastructure and few teaching staff. Alexiewicz was awarded a doctorate in July 1945 on the basis of his thesis which had been examined in Lwów. Over the next few years he had to work extremely hard, with an exceptionally heavy teaching and administrative load, to continue to undertake research which would allow his career to move forward. He submitted his habilitation thesis

*On the Denjoy integral of abstract functions*to the University of Poznań in 1948 and became a docent at the university. It is in this work that Alexiewicz introduced the 'Alexiewicz norm', which is an integral norm that makes a certain space of integrable functions into a topological vector space. In fact, because of the disruption caused by the war, his habilitation thesis was published before his doctoral thesis, but he had already a number of earlier publications such as: (with W Orlicz)

*Remarque sur l'équation fonctionelle*$f (x + y) = f (x) + f (y)$ Ⓣ (1945);

*Linear operations among bounded measurable functions I and II*(1946);

*On Hausdorff classes*(1947);

*On multiplication of infinite series*(1948); and

*Linear functionals on Denjoy-integrable functions*(1948).

In 1953 Alexiewicz was promoted to associate professor, becoming an ordinary professor in 1961 after a reorganisation had taken place at the University of Poznań. In the academic year 1961-62 the chair of mathematics at Poznań was divided into two: the Chair of Mathematics I, headed by Orlicz and the Chair of Mathematics II, headed by Alexiewicz. In 1970 there was a major reorganisation of Polish universities. The affect of these changes on mathematics at Poznań was to combine the two Chairs of Mathematics with the Chair of Logic. A new Institute of Mathematics was created, its first head being Alexiewicz who held this position until he retired in 1987.

During his time at Poznań, Alexiewicz held a number of important positions in the university. From 1951 to 1954 he served as associate dean of the Faculty of Mathematics, Physics and Chemistry, then serving as dean in 1954-55. He was elected vice-rector of the Adam Mickiewicz University of Poznań serving in this role between 1956 and 1959, a position where the candidate was chosen by popular vote among the academic community. We should also mention his work with the Poznań branch of the Polish Mathematical Society. He served as president of this branch for several years. In particular in 1955-56 he, together with three of his colleagues, formed a regional Poznań committee of the Society to oversee the organisation of the Seventh Polish Mathematical Olympiad for secondary schools.

We have indicated above some of the mathematical areas that Alexiewicz worked on. Let us quote from [7] the main areas of his research:-

Scalar and vector measurable functions; sequences of linear operators; the Denjoy integral; differentiation of vector functions; differential equations and equations with vector functions; two norm spaces and two norm algebras and their applications in summability theory; analytic functions; and applications of functional analysis to classical problems of mathematical analysis.He wrote two important Polish language texts:

*Differential geometry*(1966, second edition 1970) and

*Functional analysis*(1969). The second of these, the first major Polish text on functional analysis after Stefan Banach's

*Teoria operacyj*:-

... presents the basic theory of Banach spaces, rich material on non-locally convex and non-measurable linearly topological spaces and numerous examples of applications of functional analysis.The authors of [7] sum up his mathematical contributions as follows:-

The scientific output of Andrzej Alexiewicz indicates his immense creativity and intellectual power. It reveals his ability to understand the core of a problem, grasp the inter-relations and dependencies between different notions, and solve natural, well-motivated problems in a clear and elegant way.However, mathematics was not the only passion for Alexiewicz and his son Władysław writes in [3] about his father's passion for painting and music:-

Art played a special role in the life of Andrzej Alexiewicz. His greatest passions were mathematics, painting and music. He painted whenever he could. He would take his easel when going for walks outside Poznań, on holidays at the seaside or in the mountains, where he worked in unique places that he found. He often made sketches to fix colours and landscapes so that he was able to remember them later in his university office which he had partially converted into a studio. In his house, pictures on walls often changed but the most important place was always occupied by a beautifully framed large oil-landscape from Czarnohora, painted in 1935. The painting presented the waterfall "Huk" in Kosmacz, one of the favourite places of professor Alexiewicz. The professor was especially fascinated with the continually changing colours of the sea and the sky, with conversations with curious tourists as he set up his easel on beaches in Mielno, Dziwnow or Kolobrzeg, and on family walks at sunrises and sunsets by the Baltic sea. He painted numerous views of the sky and sea-waves, often presented in abstract forms. He also fixed his vision of the world in many mountainous landscapes from the Eastern Carpathians, the Tatras, the Pieniny and California, and also in numerous pictures painted directly out of windows of his studio. In those last landscapes he showed unknown Poznań, its plants, the changeable lights and colours of seasons of the year in the city. ... Professor Andrzej Alexiewicz had a discerning musical taste. He appreciated classical symphonic music, especially compositions of Johann Sebastian Bach, whom he held to be the greatest composer. He often went to concerts with the whole family to the University hall. The professor especially enjoyed the famous film "Amadeus" by Milo Forman. He saw it many times, encouraged all his friends to see it and later asked about the number of visits in the cinema. After his seminars and lectures he often invited students to listen to music together in his office. He also listened to music while painting. Sometimes after an especially successful symphonic concert he would go to his studio, where he, touched by music, started to paint. He was always interested in the opinions of guests about his paintings. He was very glad when his studio was visited by painters and he could hold discussions with them.

### References (show)

- L Drewnowski and Z Palka (eds.),
*Seria Mathematica Andreae Alexiewicz*(University of Adam Mickiewicz, Poznań, 1996). - Z Palka (ed.),
*The mathematical school of Poznań*(Polish) (Uniw. Mickiewicza Poznań, Poznań, 1995). - W Alexiewicz, Painting and music in life of my father, in
*Serta Mathematice Andreae Alexiewicz*(University of Adam Mickiewicz, Poznań, 1996), 15-17. - A Alexiewicz, F Baranski and J Koronski, The Mathematics-Physics Students Circle at the Jan Kazimierz University in Lwów,
*Zesz. Nauk. Uniw. Opol. Mat*.**30**(1997), 9-42. - J Musielak, Andrzej Alexiewicz - his life and work,
*Funct. Approx. Comment. Math.***17**(1987), 2-9. - J Musielak and W Wnuk, Andrzej Alexiewicz (1917-1995) (Polish),
*Wiadomosci Matematyczne***32**(1996), 153-163. - J Musielak and W Wnuk, Andrzej Alexiewicz (1917-1995), A biography, in
*Function spaces VIII***79**(Polish Academy of Sciences, Warsaw, 2008), 11-20.

### Additional Resources (show)

Other websites about Andrzej Alexiewicz:

Written by J J O'Connor and E F Robertson

Last Update January 2013

Last Update January 2013