Alexandra Bellow (née Bagdasar; previously Ionescu Tulcea; born 30 August 1935) is a Romanian-American mathematician, who has made contributions to the fields of ergodic theory, probability and analysis.

in mathematics from the University of Bucharest in 1957, where she met and married her first husband, mathematician Cassius Ionescu-Tulcea.

She accompanied her husband to the United States in 1957 and received her Ph.D. from Yale University in 1959 under the direction of Shizuo Kakutani with thesis Ergodic Theory of Random Series.

[1] After receiving her degree, she worked as a research associate at Yale from 1959 until 1961, and as an assistant professor at the University of Pennsylvania from 1962 to 1964.

During her marriage to Cassius Ionescu-Tulcea (1956–1969), she and her husband co-wrote many papers and a research monograph on lifting theory.

Alexandra's second husband was the writer Saul Bellow, who was awarded the Nobel Prize in Literature in 1976, during their marriage (1975–1985).

Alexandra features in Bellow's writings; she is portrayed lovingly in his memoir To Jerusalem and Back (1976), and, his novel The Dean's December (1982), more critically, satirically in his last novel, Ravelstein (2000), which was written many years after their divorce.

[2][3] The decade of the nineties was for Alexandra a period of personal and professional fulfillment, brought about by her marriage in 1989 to the mathematician Alberto P. Calderón.

Lifting theory, which had started with the pioneering papers of John von Neumann and later Dorothy Maharam, came into its own in the 1960s and 1970s with the work of the Ionescu Tulceas and provided the definitive treatment for the representation theory of linear operators arising in probability, the process of disintegration of measures.

[f] In the early 1960s she worked with C. Ionescu Tulcea on martingales taking values in a Banach space.

[g] In a certain sense, this work launched the study of vector-valued martingales, with the first proof of the ‘strong’ almost everywhere convergence for martingales taking values in a Banach space with (what later became known as) the Radon–Nikodym property; this, by the way, opened the doors to a new area of analysis, the "geometry of Banach spaces".

These ideas were later extended by Bellow to the theory of ‘uniform amarts’,[h] (in the context of Banach spaces, uniform amarts are the natural generalization of martingales, quasi-martingales and possess remarkable stability properties, such as optional sampling), now an important chapter in probability theory.

In 1960 Donald Samuel Ornstein constructed an example of a non-singular transformation on the Lebesgue space of the unit interval, which does not admit a

It shows, by methods of Baire category, that the seemingly isolated examples of non-singular transformations first discovered by Ornstein and later by Chacón, were in fact the typical case.

Beginning in the early 1980s Bellow began a series of papers that brought about a revival of that area of ergodic theory dealing with limit theorems and the delicate question of pointwise a.e.

This was accomplished by exploiting the interplay with probability and harmonic analysis, in the modern context (the Central limit theorem, transference principles, square functions and other singular integral techniques are now part of the daily arsenal of people working in this area of ergodic theory) and by attracting a number of talented mathematicians who were very active in this area.

One of the two problems that she raised at the Oberwolfach meeting on "Measure Theory" in 1981,[j] was the question of the validity, for

Bourgain was awarded the Fields Medal in 1994, in part for this work in ergodic theory.

It was Ulrich Krengel who first gave, in 1971, an ingenious construction of an increasing sequence of positive integers along which the pointwise ergodic theorem fails in

Later she was able to show[l] that from the point of view of the pointwise ergodic theorem, a sequence of positive integers may be "good universal" in

A place in this area of research is occupied by the "strong sweeping out property" (that a sequence of linear operators may exhibit).

Bellow and her collaborators did an extensive and systematic study of this notion, giving various criteria and numerous examples of the strong sweeping out property.

[m] Working with Krengel, she was able[n] to give a negative answer to a long-standing conjecture of Eberhard Hopf.

Later, Bellow and Krengel[o] working with Calderón were able to show that in fact the Hopf operators have the "strong sweeping out" property.

[q] Several mathematicians (including Bourgain) worked on problems posed by Bellow and answered those questions in their papers.