# Igor Stefan Kluvánek

### Born: 27 January 1931 in Košice, Czechoslovakia (now Slovakia)

Died: 24 July 1993 in Bratislava, Slovakia

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**Igor Kluvánek**was born in Košice, which had become part of Czechoslovakia in 1920. However, it was a Slovak town and there was a strong movement for an independent Slovakia which was stalled by Hungarian occupation in 1938 and World War II which followed. Igor's father was F Kluvánek and we should note, because it is relevant to Igor's life and career, that the family were Roman Catholics. Igor had a younger brother Pavol who also went on to become a mathematician. They were, as Pavol said [8]:-

Igor studied at the gymnasium at Rimavská Sobota. There he was in the same class as Eva Seress, the daughter of D Seress. Igor married Eva on 11 November 1952; they had five children, one son and four daughters.... two brothers growing up in one normal family.

After graduating from the Gymnasium, Kluvánek entered the Slovak Polytechnic University, Bratislava, where he studied for a degree in electrical engineering. He graduated in 1953 having specialised in vacuum technology. However, he had supported himself financially by working as a part-time tutor in the Department of Mathematics in the Faculty of Electrical Engineering from 1951 to 1953 while he was studying for his degree. After graduating, in 1953 he was appointed as a lecturer at the Slovak Polytechnic University. We should also note that 1953 was the year in which the Slovak Academy of Sciences was set up in Bratislava and Kluvánek began undertaking research for his C.Sc. degree from the Academy.

While he was studying at the university, his brother Pavol was still a High School student. Pavol recalled in [5] how Igor's visits back to his home had influenced Pavol's decision to study mathematics at university. After graduating from the High School, Pavol went to Bratislava to study mathematics at the Slovak Polytechnic University. By this time Igor was married but Pavol lived with his family in Bratislava. He said [8]:-

Lev Bukovsky was a student at a high school in Bratislava in 1955 and he told a nice story in [3] about his first meeting with the Kluvánek brothers:-After my departure from home I found at his family home in Bratislava an extremely careful and safe asylum. Moreover, in the person of Igor, I found a permanent consultant for my studies.

In 1956 Kluvánek was promoted to the equivalent of a Senior Lecturer at the Slovak Polytechnic University. In 1961 he published, in collaboration with Ladislav Misik and Marko Svec, the two-volume textbookAt our school a great teacher of mathematics taught, professor Ondrej Gábor, who produced many mathematicians. I also owe him for having brought me to mathematics. He had the habit of inviting some mathematicians to teach an hour of mathematics. And once he invited two brothers Igor and Pavol Kluvánek. Pavol stood modestly in a corner and Igor addressed us in his typical manner. He asked the class, "What is the square root ofa^{2}?" He got the answer, "It's plus and minus a." Typical Kluvánek reaction: either way, one is Igor and one is Pavol. This stayed with me.

*Matematika: Pre studium technickych vied*Ⓣ. This proved a very popular text with a second edition published in 1963 and a third edition in 1966. The book, covered Differential and Integral calculus, Analytic geometry, Differential equations and Complex variable [14]:-

Czechoslovakia had been governed by a Communist regime since 1948 and, although the majority of Slovaks were Roman Catholic, there was an official government policy of atheism. Kluvánek was a practicing Roman Catholic and this was seen as incompatible with his role as a teacher. However, although the authorities discriminated against Kluvánek because of his religion, as they did against others in a similar position, the situation was tolerated. It made his position uncomfortable from 1961 onwards, but he was still able to carry out his duties. It did delay for a year the award of his C.Sc. degree which he did not receive until 1962. He had published papers in Slovak, Czech and Russian. For example:This textbook marked a breakthrough in the teaching of mathematics in the Czechoslovak technical universities and is used today.

*On systems of sets closed with respect to certain set operations*(Slovak) (1955);

*Abstract integral as a positive functional and the theorem on extension of measure*(Czech) (1956);

*On vector measure*(Slovak) (1957); and

*On the theory of vector measures*(Russian) (1961).

Pavol Josef Safarik University was founded in Košice in 1959 and, in 1963, Kluvánek was appointed to the Department of Mathematical Analysis at the new University. He was invited to Flinders University of South Australia soon after the university was founded in Adelaide in 1966. He was unsure whether to accept, and hesitated for quite some time discussing the offer with his friends. Some of his friends said that if he went to Australia with his family they were sure he would not return to Czechoslovakia but Kluvánek was adamant that he would not stay more than two years in Australia. He obtained the necessary permission from the Czechoslovakian authorities and, together with his wife and five children, went to Australia in March 1967. He had a two-year visiting position at Flinders University but, on 20 August 1968, his wife and children flew back to Czechoslovakia so that the children would be back in time to begin the new school year. However, events had been moving fast in Czechoslovakia where Alexander Dubcek was implementing many economic and political reforms. On 15 July Dubcek was warned by a special meeting of the Warsaw Pact powers that they believed that a revolution was taking place and it was their duty to prevent it. Dubcek believed he could talk his way out of the difficult situation but, on the evening of 20 August 1968, Soviet, East German, Polish, Hungarian, and Bulgarian troops entered Czechoslovakia. Links with the outside world were severed and the plane carrying Kluvánek's wife and children landed in Zürich and could not continue. They had no visas to enter Switzerland, or any other country for that matter. Returning them to Australia was an option, but this required fares to be paid and Flinders University did not want to pay their fares nor did Safarik University in Košice. Eventually the problem of finance was sorted out and they returned to Adelaide.

However, this was far from the end of Kluvánek's problems. He was sentenced in his absence to two years in prison by the Czechoslovakian authorities for failing to return. His wife was sentenced to one year in prison and all their possessions, including their home in Košice, were confiscated. He only had permission to say in Australia until 1969 when his temporary position ended. However, Flinders University of South Australia agreed to appoint him as Professor of Applied Mathematics in the School of Mathematical Sciences in 1969 and his difficult situation was resolved. Some of the important papers he published while working in Australia are:

*Fourier transforms of vector-valued functions and measures*(1970);

*On the product of vector measures*(1973);

*The range of a vector-valued measure*(1973); (with Greg Knowles)

*Liapunov decomposition of a vector measure*(1974); and (with Greg Knowles)

*Attainable sets in infinite-dimensional spaces*(1974).

In 1975, in collaboration with Greg Knowles, Kluvánek published the monograph

*Vector measures and control systems*. J J Uhl, Jr writes in a review:-

The review [15], also by J J Uhl, Jr, ends with the following paragraph:-This is a monograph on the geometry of the range of a vector measure and applications to control systems governed by partial differential equations. Completely self-contained, the book starts with a thorough discussion of integration with respect to a vector measure. Then the authors employ a time-honoured method for the study of the properties of a vector measure by studying the properties of the mapping induced by a vector measure as an operator on the space of its integrable function. After this, they introduce and study the concept of a closed vector measure with its value in a locally convex space. Every vector measure whose range is in a Banach space is a closed measure, and the authors show that closed vector measures have a structure rich enough for intrinsic interest and applications. ... This splendid book gives much more extensive treatment of the range of a vector measure than other available books ... Moreover, it opens the new area of applications of vector measures to control systems governed by partial differential equations. It is a must for anyone interested in the theory of vector measures.

In 1988 Kluvánek published the monographThere are several reasons to be thankful for this book. In addition to bridging the gap between pure and applied mathematics, it is the definitive work on the range of a vector measure. It reads easily and its literature surveys(which appear at the end of each chapter)are chock-full of tidbits of information that are useful to the student, scholar or researcher. It is a book worth having and using.

*Integration structures*. W A J Luxemburg writes in a review:-

To illustrate Kluvánek's views on teaching mathematics, let us quote from his paperThe subject matter of the monograph under review is motivated by the fact that in describing superpositions of evolution processes one often encounters serious problems in solving the corresponding evolution equations. Indeed, to express the required solutions in integral form one may have to integrate with respect to a vector-valued measure of infinite total variation. For this reason the author asks whether an integration method with respect to a sufficiently "wild" set function of infinite total variation and for which a Fubini-type theorem holds can be developed and applied to solve the above-mentioned problem. ... The monograph is warmly recommended to all analysts working in the area of general, not necessarily absolute, integration theory and its applications.

*What is wrong with calculus?*written in 1988:-

Kluvánek's wife Eva died in 1981. In 1986 he resigned his chair at Flinders University and during 1987-88 studied at St Dominic's, a Roman Catholic Seminary in Camberwell, Melbourne. Earlier, in 1982, he had studied at St Paul's Roman Catholic Seminary in Kensington, Sydney. While at Dominic's he wroteThe common view has it that, whatever there was to be done in this respect, was already taken care of by people like Cauchy, Bolzano, Weierstrass and their contemporaries. While there is a substantial element of truth in this view, it is not the whole truth ... I will try and indicate some themes that still deserve our attention. In particular, I wish to suggest that the role of the notion of limit in elementary teaching can and should be substantially reduced. ... Since its invention, the foundations of the differential and integral calculus were clarified and also the techniques were improved. And that gives us a key for the understanding of the deficiencies in the teaching of 'calculus'. The processes of clarification, simplification and improvement stopped at a certain stage and/or were confined to some aspects of the differential and integral calculus.

*Human cognition and the idea of judgement in the fourth gospel*, and

*Realism, freedom and the renewal of the church*. However, he returned to mathematics with a temporary appointment at the Centre for Mathematical Analysis in Canberra, Australia. He also spent some time at Macquarie University. In 1989, with major changes taking place in Czechoslovakia, Kluvánek returned to Košice. His children, by then adults, remained in Australia. The events of 17 November 1989 are described by

*Encyclopaedia Britannica*as follows:-

Lev Bukovsky wries in [3]:-On November17the authorities allowed a demonstration commemorating the5040^{th}anniversary of the brutal suppression of a student demonstration in German-occupied Prague. The recurrence of police brutality at the anniversary observance set off a protest movement that gained particular strength in the country's industrial centres. Pro-democracy demonstrations and strikes continued nationwide ... Vaclav Havel served as chief spokesman. It was Havel who in late December became Czechoslovakia's first non-communist president in more thanyears following the resignation of the communist government and his election to the office by a parliament still dominated by communist deputies.

Kluvánek, as someone who had been persecuted by the Communist regime, became something of a star in the new Czechoslovakia. He was even offered the position of Minister of Education in the new government, but declined. In 1990 he was appointed to the Slovak Technical University in Bratislava, and he also taught at Comenius University in Bratislava. Sadly he did not live long in this final stage of his life but he did marry for a second time during these last years.On Friday17November1989Igor Kluvánek sat in our apartment in Košice, with many of those who had met before he went to Australia sitting there as well. We did not have time to watch the event. It wasn't until Monday we found out that something was happening. Some of our politicians also missed that something was happening, but we just were so absorbed with Igor Kluvánek that we didn't see new Europe beginning.

Rodney Nillsen writes about Kluvánek's personality in [7]:-

Let us end by quoting the final sentence from Rodney Nillsen's article [7]:-Igor had definite views on many things, and he could express those views in a very definite manner. There were people who sometimes regarded him as overbearing. He was often controversial and not necessarily popular. But he could also show great support for and loyalty to people. In ordinary conversation, Igor had a great enthusiasm for ideas, discussion and debate, which he often conveyed with a characteristic emphasis, frequently combined with humour. He achieved moments of great enthusiasm and intensity in his lectures and seminars, and he conveyed the feeling that the ideas were really significant, not because they came from him, but because of their intrinsic value and qualities. ... Socially, Igor could be charming and entertaining, and show an interest in people's lives and concerns. He was a complex personality whose adherence to principles and to the seriousness of ideas made him an inspiration to many who knew him.

In times where the serious life of the mind struggles to exist in the corporate institutions which universities in the West have become, Igor's life and example, with their dedication to principle and truth in their broadest senses, involving the whole person, remain inspiring.

**Article by:** *J J O'Connor* and *E F Robertson*

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