Shmuel Kantorovitz

Shmuel Kantorovitz

Professor Emeritus of Mathematics

Email: kantor@math.biu.ac.il
Phone: +972-3-531-7875 (dept. office); +972-3-936-3348 (home).
Fax: +972-3-936-3348
Office: Computer and Mathematics Bldg (216), Room 121
Updated Nov 15, 2017


Birthdate: September 17, 1935.

ACADEMIC STUDIES

1951-1955: Hebrew University, Jerusalem, Israel. M.Sc. in Mathematics,
April 1956.
1960-1962: University of Minnesota, Minneapolis, Minn., USA. Ph.D. in
Mathematics, June 1962.

POSITIONS

1956-1960: Mathematician for the Government of Israel.
1960-1962: Instructor at the University of Minnesota, Minneapolis, Minn.
1962-1963: Instructor at Princeton University, Princeton, NJ.
1963-1964: Visiting Member at the Institute for Advanced Study, Princeton, NJ.
1964-1967: Assistant Professor at Yale University, New Haven, Conn.
1967-1970: Associate Professor at the University of Illinois, Chicago, Il.
1970-1978: Professor at the University of Illinois, Chicago, Il.
1972-2003: Professor at Bar-Ilan University, Ramat-Gan, Israel.
2003-present: Professor Emeritus, Bar-Ilan University, Ramat-Gan, Israel.

VISITING POSITIONS

Summer 1978: University of Toronto, Queens University, and Dalhousie
University, Canada.
Summer 1980: Mathematics Research Institute, ETH, Zurich.
September 1980-December 1981: Temple University, Philadelphia, PA.
Summer 1982: Mathematics Research Institute, ETH, Zurich.
Summer 1983: Purdue University, West Lafayette, Indiana.
Summer 1986: University of Pennsylvania, Philadelphia, PA.
Summer 1987: Temple University, Philadelphia, PA.
February 1988: Mathematics Research Institute, ETH, Zurich.
Summer 1988: Bryn Mawr College, Bryn Mawr, PA.
September 1990-July 1991: Ohio University, Athens, Ohio.
September 1999-August 2000: the University of Illinois, Chicago.

ADMINISTRATION

1977-1979 and 1985-1987: chairman of the Department
of Mathematics and Computer Science at Bar-Ilan University.

AREA OF RESEARCH

Spectral Theory of operators in Banach space;
Semigroups of operators.

PH.D. DISSERTATIONS completed under my direction:

M.S. Smith, On automorphism groups of C*-algebras, Yale University, 1968.
Published in Trans. Amer. Math. Soc. 152 (1970), 623-648.
K.J. Pei, Generalized Volterra operators. The University of Illinois,
Chicago, 1972. Published as joint paper:
S. Kantorovitz and K.J. Pei, Pairs of operators satisfying the
Volterra commutation relation, Indiana Univ. Math. J. 23 (1974), 1177-1197.
R.J. Hughes, Semigroups of unbounded linear operators in Banach space.
The University of Illinois, Chicago, 1975. Published in
two papers:
1. Semigroups of unbounded linear operators in Banach space, Trans.
Amer. Math. Soc. 230 (1977), 113-145.
2. On the convergence of unbounded sequences of semigroups, J. London
Math. soc. (2) 16 (1977), 517-528.
A. Viselter, The multidimensional fractional moment problem and spectral
representation of local symmetric semigroups of operators, Bar Ilan University,
Israel (2009). Published in three papers:
1. Generalized Widder theorem via fractional moments, J. Funct. Anal. 256
(2009), 594-602.
2. Spectral representation of local semigroups of operators, Semigroup Forum
79 (2009), 355-368.
3. Spectral representation of local semigroups of operators over topological
groups, Acta Sci. Math. (Szeged) 78 (2012), 291-314.


BOOKS and MONOGRAPHS

1. Spectral Theory of Banach Space Operators, Lecture Notes in Math.
No. 1012, Springer-Verlag, 1983 (v+179pp.)
2. Semigroups of Operators and Spectral Theory, Pitman Research Notes
in Math. Series, No. 330, Longman, 1995 (iii+135pp.)
3. Introduction to Modern Analysis, Oxford Graduate Texts in Math.
No. 8, Oxford University Press, Oxford 2003 (434 pp.)
4. 2nd edition of #3, in paperback, Oxford University Press, Oxford 2006
(434 pp. + 200 pp. of solutions on companion website.)
5. Topics in Operator Semigroups, Progress in Mathematics No. 281,
Birkhauser, Boston Basel Berlin 2010, xiii+266 pp.

6. Several Real Variables, Springer 2016 (xii+307 pp.)

link ERRATA SHMUEL KANTOROVITZ
RESEARCH PUBLICATIONS

1. Two-dimensional distributions with given marginals (with S. Kotz),
Riveon Lematematica 11 (1956), 32-38, 91.
2. On the integral equation ..., Riveon Lematematica 12 (1957), 24-26.
3. A note on partial linear integral equations, Bulletin Res. Coun. Israel
7F (1958), 181-186.
4. Une propriete de l'approximation spherique dans un probleme d'energie
minimale. Bulletin Res. Coun. Israel 7F (1958), 149-154.
5. The annihilator of a closed ideal in a function algebra, Bulletin Res.
Coun. Israel 9F (1960), 132-134.
6. An operational calculus and spectral operators, Ph.D. dissertation,
University of Minnesota, June 1962.
7. Operational calculus in Banach algebras for algebra-valued functions,
Trans. Amer. Math. Soc. 110 (1964), 519-537.
8. On the characterization of spectral operators, Trans. Amer. Math. Soc.
111 (1964), 152-181.
9. Classification of operators by means of the operational calculus,
Bulletin Amer. Math. Soc. 70 (1964), 316-320. (Research announcement.)
10. (Full version of #9), Trans. Amer. Math. Soc. 115 (1965), 194-224.
11. A Jordan decomposition for operators in Banach space, Bulletin
Amer. Math. Soc. 71 (1965), 891-893. (Research announcement.)
12. (Full version of #11), Trans. Amer. Math. Soc. 120 (1965), 526-550.
13. The semi-simplicity manifold of arbitrary operators, Trans. Amer. Math.
Soc. 123 (1966), 241-252.
14. Local C^n-operational calculus, J. Math. and Mech. 17 (1967), 181-188.
15. The C^k-classification of certain operators in L^p, Trans. Amer.
Math. Soc. 132 (1968), 323-333.
16. The C^k-classification of certain operators in L^p. II, Trans. Amer.
Math. Soc. 146 91969), 61-67.
17. On the operational calculus for groups of operators, Proc. Amer. Math.
Soc. 26 (1970), 603-608.
18. Commutators, C^k-classification, and similarity of operators,
Trans. Amer. Math. Soc. 156 (1971), 193-218.
19. Formule exponentielle pour les element Volterra d'une algebre de
Banach, C.R. Acad. Sc. Paris 274 (1972), 1876-1877.
20. Spectral equivalence and Volterra elements, Indiana Univ. Math. J. 22
(1973), 951-957.
21. Commutation de Heisenberg-Volterra et similarite de certaines
perturbations, C.R. Acad. Sc. Paris 276 (1973), 1501-1604.
22. Pairs of operators satisfying the Volterra commutation relation,
Indiana Univ. Math. J. 23 (1974), 1177-1197 (with K.J. Pei).
23. Representation of C^n-operators, Proc. Amer. Math. Soc. 48 (1975),
152-156 (with K.J. Pei).
24. Characterization of C^n-operators, Indiana Univ. Math. J. 25 (1976),
119-133.
25. Similarity of certain operators in l^p, Proc. Amer. Math. Soc 67 (1977),
99-104.
26. Intertwining certain operators in l^p, J. London Math. Soc. (2) 16
(1977), 514-516.
27. Boundary values for holomorphic semigroups of unbounded operators
and similarity of certain perturbations, J. Functinal Anal. 29 (1978),
253-273 (with R.J. Hughes).
28. Similarity of certain singular perturbations in Banach space,
Proc. London Math. Soc. 42 (1981), 362-384 (with R.J. Hughes).
29. Characterization of unbounded scalar-type operators with spectrum in
a half-line, Comm. Math. Helv. 56 (1981), 163-178.
30. Spectrality criteria for unbounded operators with real spectrum,
Math. Ann.256 (1981), 19-28.
31. Spectral representation of local semigroups, Math. Ann. 259 (1982),
455-470 (with R.J. Hughes).
32. Quasi-affinity in certain classes of operators, Bulletin London Math.
Soc. 19 (1987), 449-457 (with R.J. Hughes).
33. Volterra systems of operators, J. Math Anal. and Appl. 133 (1988),
135-150.
34. Spectral representations for unbounded operators with real spectrum,
Math. Ann. 282 (1988), 535-544 (with R.J. Hughes).
35. The Hille-Yosida space of an arbitrary operator, J. Math. Anal. and
Appl. 136 (1988), 107-111.
36. Spectral analysis of certain operator functions, J. Operator Theory 22
(1989), 243-265 (with R.J. Hughes).
37. Examples on similarity in L^p, J. Math. Anal. and Appl. 180 (1993),
550-552.
38. C^n-operational calculus, non-commutative Taylor formula, and
perturbation of semigroups, J. Functional Anal. 113 (1993), 139-152.
39. Laplace and Laplace-Stieltjes space, J. Functional Anal. 116 (1993),
1-61 (with R. deLaubenfels).
40. Sur le calcul fonctionnel dans les algebres de Banach, C.R. Acad.
Sc. Paris 317 (1993), 951-953.
41. The semi-simplicity manifold on arbitrary Banach spaces, J. Functional
Anal. 133 (1995), 138-167 (with R. deLaubenfels).
42. On Liu's analyticity criterion for semigroups, Semigroup Forum 53
(1996), 262-265.
43. Analytic families of semigroups, Semigroup Forum 54 (1997), 356-363.
44. Renorming method in spectral theory, Dynamics of Cont., Discrete,
and Impulsive Systems 6 (1999), 413-443.
45. Analytic families of evolution systems, Acta Sci. Math. (Szeged) 65
(1999), 311-318 (with M. Mahadav).
46. Asymptotics of analytic semigroups, Semigroup Forum 62 (2001), 473-476.
47. Mean stability of semigroups, Taiwanese J. Math. 6 (2002), 89-103
(with S. Piskarev).
48. Asymptotics of analytic semigroups. II, Semigroup Forum 68 (2004),
308-310.
49. Asymptotics of resolvent iterates for abstract potentials,
Semigroup Foprum 68 (2004), 491-494.
50. Cauchy estimates for the operational calculus, Int. J. Pure Appl.
Math. 21 (2005), 497-500.
51. Abstract Volterra relation, Semigroup Forum 75 (2007), 359-387
(with A. Viselter).
52. Generators of regular semigroups, Glasgow Math. J. 50 (2008), 47-53.
53. Similarity of operators associated with the Volterra relation,
Semigroup Forum 78 (2009), 285-292.
54. Compact commutators of the Cauchy transform, Acta Sci. Math. (Szeged), 76
(2010), 165-171.
55. Characterization of the Volterra operator and the Riemann-Liouville
semigroup, Acta Sci. Math. (Szeged), 80 (2014), 459-466.
56. Characterization of the Gamma semigroup, Semigroup Forum 95 (2017),
251-258.
Solutions of Exercises in Introduction to Modern Analysis:
http://www.oup.co.uk/academic/companion/mathematics/kantorovitz